"The fewer chances I have to drink, the less I drink" is correct and natural. You are using "chance" correctly in one of its meanings: "opportunity."

The fewer opportunities I have to drink, the less I drink.

Saco, colloquially, you would express it this way: "Because I drink less often, I can't drink as much now as I used to". This is a good way of expressing it as it is saying EITHER you get drunk easier so have to drink less, OR you simply can't physically drink as much because your stomach, etc isn't used to it.

Thank you for your comment and correcting my sentences Ally, I meant I hardly drink at all now and the amount that I can drink has decreased. Thank you so much Greg, That's what I wanted to say! now I have a better understanding of comparatives.

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?