If my uncle promised to pay for law school if I got my bachelor’s degree and did not drink or do drugs, can he now renege after a falling out?

You need to consult with an attorney about this situation; he or she needs to review all the facts and circumstances in detail.

Usually, a unilateral promise to something for someone is not enforceable--e.g. a parent could promise to pay for law school, and not be held accountable for  it. However, if the promisee--that's you--gave "consideration" for the promise, that could transform it into an enforceable agreement. Usually, consideration is something of value to the other party--e.g. if your uncle had promised that if you worked in his office or store on weekends while in college, he'd pay for lawschool, that would constitute a contact or agreement. However, there are some cases where something which does not directly benefit the promisor (your uncle) and even which are themselves things the promisee ought to do anyway (i.e. getting a bachelors, not drinking and not doing drugs, are all good things in and of themselves) will constitute valid consideration, since you are changing your behavior in response to your uncle's offer, to do what he wants you to do.

Complicating this situation is that some contracts or agreements, even if they would otherwise be valid and enforceable, need to be in writing. I believe that in IL, if the agreement will take more than 1 year to perform--like getting a bachelors degree--it must be in writing, which could possibly bar your enforcement  of the promise. That said, there are sometimes ways to get around that requirement, depending on the facts.

The short answer is: the promise *may* be enforceable, but it is likely something of an uphill battle to do so, if there is a lack of writing on it and because of the nature of the consideration. However, given how much is at stake, it would be worthwhile to consult in person with an attorney. Good luck.