As Dan wrote, it makes complete sense. Chance/chances is a countable noun so the use of "fewer" is correct. Your explanation can be better worded though.
You wrote: I mean that I used to drink a lot with my friends, but recently I don't have chances to drink than before. Then it makes me able to drink less than before.
Better: I mean that I used to drink a lot with my friends, but recently I don't have as many chances to drink with them as before. As a result, I drink less than I used to.
Also, 『お酒が飲めなくなってくる。』implies you don't drink at all anymore, or hardly drink at all...is that what you want to say?