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!")