score:6
You officially need to keep it until you leave the country. It seems however that many people lose it and it might not even be asked when you exit the country (plus the paper might have faded out which makes it even less useful). You can get a replacement before leaving the country at the Santiago airport.
Also, in some accommodations, you can avoid paying the local VAT (of 19%) if you are staying as a tourist and pay for your accommodation using US dollars and show this Tarjeta unica migratoria
and an ID.
See this related and useful answer about getting a replacement card.
Upvote:6
While Vince's answer is entirely right, and you must have it until you exit the country, let me add that you must give it back to PDI at that time, so you can't actually keep it after you leave. Good thing or I'd have a few dozens at home by now!