Uh oh. I can see some are not going to like this post. It is in early game context. The way I most often defeat chariots is with cavalry... light cavalry, plus generals.
Make no mistake... light cavalry can get butchered by the scythed chariots in particular, but like all battles, one must know the enemy, terrain, and self.
Chariots get top attention in most cases, and since I run an army built on cavalry and mobility, I have the units maneuvered and ready to attack. The stategy is failry simple in concept, but sometimes difficult in execution: attack in large numbers from many directions, simultaneously, and get the h*ll out of the way then they run amok, or dogpile them and kill immediately. I usually do the latter. Hesitation, or non-committal, and your cavalry get butchered (Equites, in the case of Romans). I also use any nearby infantry units to zero in and attack. In essense, it's really just a "everyone dogpile the chariots" strategy, but it works, and it works with relatively few casualties. If you nibble at chariots, then your losses go way up. Dogpile.
There is one case I've found that really does not work even when implementing the dogpile method with cav, and thats when you dogpile elephants. Heck, Equites even die when pursuing routing elephants. But for chariots, it works... if you properly commit and execute. PS, If you are new to the game, do not use cav in the way I describe unless you are willing to risk the high casualties others have posted about. It does take a few times of experience to minimize losses...