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The short answer is that Constantine didn't create the Chi-Rho Christogram. There is evidence that it was already being used before Constantine, but he certainly raised the symbol's prominence after the Battle of Milvian Bridge in 312AD.
Most of the early Christian texts were written in Greek, and Greek actually continued as the language of the eastern Roman, or "Byzantine", Empire. It was therefore natural that the symbol would have derived from the first two letters of the Greek word ΧΡΙΣΤΟΣ.
You are right that Latin was the language of Constantine's court, but as an educated Roman he would probably have known some Greek, and he was probably aware of some of the Christian symbols in use at that time. He certainly wasn't fluent in the language though as he had to use an interpreter to address Greek-speaking bishops at the Council of Nicaea.
In the story of the Battle, the sign that appeared was a cross, or something similar (Lactantius is the first author to mention the story (just a couple of years after the battle), and he is not entirely clear on that point). The sign was associated with a dream in which Constantine received the message (in Latin) "In hoc signo vince!" ("In this sign, conquer!")
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Although Constantine was a Roman Emperor, he was not ethnically or genealogically Roman. His Mother, Helena, was Greek, his Father was Illyrian/Albanian and he was born and raised in the Balkans.
During his early years, Constantine, would have been exposed to the Latin, Greek and Illyrian languages, due to his geographic, demographic and familial settings. While Latin was Constantine's main language, he probably would have had a very basic knowledge/command of the Greek and Illyrian languages as well, again, due to his geographic, demographic and familial settings. So that his use/creation of the famous "Chi-rho", would not necessarily have been that foreign to him considering the fact that his Mother was Greek and that the Greek language was widely spoken and written throughout much of the Roman Empire-(including parts of the Balkans/Southeast Europe).
(Eusebius is a good source for understanding Early Church History and yes, Eusebius wrote in Greek).
(There are Wikipedia articles on Constantine which detail his biographical background).
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Constantine was ethnically Greek and Illyrian, that is to say his mother, Helena, was of ethnic Greek descent and his Father, was Illyrian-(most likely of Albanian descent).
While Constantine certainly had a Roman cultural orientation for much of his life-(particularly, with regard to the Latin language and of course having been the First "Eastern Roman" Emperor), he was also of a mixed Hellenic and ancient Balkan background, both ethnically and culturally.
(Wikipedia articles on Constantine, Helena and The Byzantine Empire).