As everyone else has already noted, if you want to watch live games your options boil down to 2 things:
1) MLB.tv streaming
2) Placeshifting through a device like a Slingbox located in the White Sox broadcast area.
No one is legally streaming MLB games outside of that - in a club's broadcast zone they have exclusive rights (which are normally sold to a Regional Sports Network), and outside of that the MLB has exclusive rights. Ultimately this really isn't even an application question, the real question you're asking is if you can get MLB games streamed for free.
Now if you want to listen to games you have a couple more options. MLB sells an audio service (Gameday Audio) for $20/year. Overall audio broadcasting rights aren't nearly as tightly held since they're not as valuable, so you may find local radio stations simulcasting the game online, but most of the time they're not supposed to be doing that so don't be surprised if you can't regularly listen to games without paying.