That is not a mistake which any native speaker would make. Your professor will have said 'I had to choose'. If the word sounded to you like 'chose', it was because of your interpretation of his or her particular accent - it would not be an error.
There are many different ways of pronouncing the 'o' and 'oo' sounds in different native-speaker accents. The vowel sounds of an English speaker brought up in the American South are very different from those of someone from the Midwest, and very different again from a Bostonian or New Yorker, for example. This is an issue of phonology, not grammar.