Can I put a 1/2" chuck on a 3/8" drill?

No. The motors and transmissions are designed to handle a specific maximum load. Replacing a 3/8" chuck with a 1/2" chuck is not recommended. Make sure when you buy your replacement chuck that you buy a chuck for the spindle size of your drill. Most drills are either 3/8"-24 or 1/2"-20.