chances?

Screwed? No way. As good a chance as "anyone?" At top tier, honestly no. It's far from impossible, but you'll have to make a very strong impression to compete with the folks who know people going in.

You didn't say if you were a guy or girl. Every sorority has plenty of out of state girls, though knowing people can go a very long way. Fraternities are trickier, as there are fewer rules about rush. For example, DKE typically takes very rich kids from a certain group of high schools. You may be in trouble there unless your dad is a Hollywood producer. Phi Gam is probably out because you aren't from east of I-95 and you probably don't wear t-shirts with pictures of ducks and fish. The rest probably wouldn't care much.

For mid-tier (and below), I doubt being from California would matter at all, guy or girl.