Who was the first retailer in Monterey, California?

To add to Aaron's answer:

The first retail store keeper in Monterey was probably Don David Spence, born 24 October 1798 in the parish of Huntly, Scotland to David Spence and his wife Helen Stewart:

(registration required to access this birth record. Due to copyright restrictions I am unable to post the image)

Scotlands People

He died 18 February 1875 in Monterey and there is a memorial to him in the Monterey City Cemetery:

https://www.findagrave.com/memorial/42878080/don-david-spence

There is a short page on the Monterey County Historical Society which has a brief summary of his life including the fact that he opened a shop in Monterey:

http://mchsmuseum.com/spence_david.html

The justification for this answer is as follows:

In November 1826 Captain F W Beechey of HMS Blossom, then anchored in San Francisco Bay, dispatched three of his officers overland to Monterey in search of supplies. In his "Narrative of a voyage to the Pacific and Beering's strait" he describes their arrival at Monterey:

https://archive.org/details/narrativeofvoyag02beec/page/56/mode/2up

(my literal transcription of the published book, hence ownward, not onward)

As they approached the town, pasture lands, covered with herds of cattle succeeded this wild scenery: and riding ownward, trees of luxuriant growth, houses scattered over the plain, the fort, and the shipping in the bay, announced the speedy termination of their journey. At five o'clock in the evening they alighted in the square at Monterey, and met a kind reception from Mr Hartnell, a merchant belonging to the firm of Begg and Co. in Lima, who was residing there, and who pressed them to accept the use of his house while they remained in the town-an offer of which they thankfully availed themselves.............

......Upon enquiry after the stores and medicines the ship stood in need of, the result was highly unfavourable; as there were no medicines to be had, and some stores which were essential to the ship could nowhere be procured. The exchange on bills was favourable, but there was no specie: Mr. Marsh therefore purchased what stores he could from the inhabitants and from the shipping in the roads..........

In January 1827 the Blossom arrived at Monterey to collect the stores that had been purchased:

We dropped our anchor in Monterey Bay on the first of January, and with the permission of the governor, D.Miguel Gonzales, immediately commenced cutting the spars we required; for each of which we paid a small sum. Through the assistance of Mr. Hartnell, we procured several things from the missions which we should otherwise have sailed without, and our thanks are further due to him for his kindness and attention during our stay.

It seems fairly clear from this that in January 1827 there was no retail store in Monterey, though the firm of McCulloch Hartnell and Company had been granted permission to build one in 1823, according to the following extract from the "The Lives of William Hartnell" by Susanna Bryant Dakin:

After the customary exchange of compliments, the Englishman[Hartnell] explained to His Excellency[the Governor] that the maintenance of a commercial house in the country necessitated freedom of more ports as well as permission to build warehouses in scattered sites along the coast. Here produce could be kept, and he needed at least one store in which to sell at retail. He also protested against excessively high duties on imports. Don Luis listened sympathetically to Don Guillermo’s[Guillermo Arnel=Hartnell] complaints. Without forcing him to endure the long wait for permission to come from Mexico City, the Governor granted to Macala[=McCulloch] y Arnel the right “to trade in all the ports of California and also in all the landfalls and bays nearest the missions.” This was a real triumph over competitors who were obliged to anchor either in San Diego or Monterey. Arguello seemed reasonable about duties, and on May 21, 1823, had acceded to the partners’ request that they be granted land and permitted to build any needed warehouses, stores, or residences in the ports of Monterey and San Pedro. So the new firm became solidly established.

Dakin also says, as Aaron has mentioned in his answer:

Early in 1823, the British firm had obtained a spacious adobe to be used as a ‘tienda.’

However there is no further mention in Dakin to suggest that a physical retail store or shop was set up nor is there any mention of such an establishment in any of the 150+ documents, mainly letters, that I have examined.

Adele Ogden, in her article "Hides and Tallow: McCulloch, Hartnell and Company 1822-1828" in the California Historical Society Quarterly of September 1927 says:

https://nuhis220a.files.wordpress.com/2018/10/hides-tallow-article-by-ogden-1927.pdf

What were the general trading methods of McCulloch, Hartnell and Company? As soon as a company ship had dropped anchor in Monterey Bay, the captain delivered to Hartnell business letters from the main firm in South America and the invoice of the ship's cargo. Shortly thereafter, circular letters, announcing the arrival of the brig and enclosing a list of goods aboard, were dispatched to the northern and southern mission fathers. Within a week or so, the recently arrived vessel proceeded southward, touching at specified collection depots. At each port samples of the ship's cargo were exhibited, goods delivered to the missions, future order lists made out by the friars, and hides and tallow taken aboard. From San Diego, where stowage was completed, the ship sailed for South America or England.

Again there is no mention of any retail store.

There is evidence though that William Hartnell was retailing, perhaps on his own account as opposed to on the partnership account, judging from this statement of John Milligan's account with William Hartnell for the period from November 30th 1822 to 10th January 1829:

https://archive.org/details/documentos2455129997vall/page/n184/mode/2up

Referring again to Dakin, Hartnell had an assistant/employee called David Spence:

The wedding of William Edward Petty Hartnell and Maria Teresa de la Guerra was planned to take place in Santa Barbara on the last day of April 1825, when the bride would be sixteen and the groom just turned twenty-seven. Don Guillermo had little time for singing and dancing with his future relatives in the spring days that preceded his wedding. In the first place, there was the necessity of preparing a proper home in Monterey for his bride of distinguished family and luxurious upbringing. He now had the aid, in this personal project as well as in company business, of a good-natured Scotsman named David Spence, sent up from Lima in September. McCulloch had introduced him as “my friend Mr. Spence, who you will find of the greatest service to you.”

And Dakin states that David Spence operated a general store in Monterey after his contract with Hartnell expired. It may be assumed that this was in late 1828 or 1829:

After Hartnell’s return from South America[in July 1828,he'd journeyed there to discuss the dissolution of the partnership] his business decreased in volume and he, by necessity, managed it alone. His former associates, McCulloch, Logan, and Fraser, no longer were in the country; and David Spence went into business for himself when his contract time expired. He stayed on in Monterey, operating a general store and engaging in various trading ventures.

So in summary it would seem that whilst McCulloch Hartnell and Company, or at least William Hartnell on his own account, were the first retailers in Monterey, David Spence was probably the first retail store or shop keeper.

May I also, as a distant cousin of (Hugh) McCulloch mentioned in Aaron's answer just correct the impression that he "split". He was writing letters with instructions to Hartnell from different missions in California until at least 14 August 1823 and on 1 March 1824 he writes from Mazatlan which he was temporarily visiting being by then based in Callao:

https://archive.org/details/documentos3305189994vall/page/n34/mode/2up

(my transcription)

I take the whole of the management of the Californian business into my own hands, having only to consult with him [John Begg] as to the disposal of the produce, chartering vessels etc. so that if you play your cards in that quarter, as well as we will ours in Peru, and our friend in England, I have no doubt we will make a very handsome thing of it, although what has come to the Lima market as yet has been a losing concern.

To quote from Dakin:

In the spring of 1824, McCulloch left the California scene for good. It was decided that the firm would benefit by one partner remaining on the coast, while the other returned to live in Lima, to supervise the selection and disposal of cargoes in South America and, only occasionally, to act as supercargo on coastal or European voyages. Hartnell was the logical choice to manage the company affairs in California, if he could conquer his old weakness.

After the business of McCulloch Hartnell and Company was wound up Hartnell failed to pay his share of the losses and on 2 June 1831 McCulloch wrote to Hartnell:

https://archive.org/details/documentos20710002vall/page/n41/mode/2up

(my transcription)

I have paid Mr Begg my full proportion of all losses and hope that some day or other you will be able to reimburse me if not for all at least part of said Acct

Also, according to Dakin, referring to Dr. Stephen Anderson, who was acting as go-between between Begg and McCulloch in Lima and Hartnell in California:

On April 15, 1833, his onetime partners gave Hartnell a full discharge of all debts. Anderson wrote this welcome news to California, with the added assurance that throughout the whole transaction McCulloch had proved himself a good friend.

I realise this last part of the answer does not relate directly to the question but I do wish to make it clear that from all accounts and by this and other actions Hugh McCulloch(1793-1842) was an honourable man.