Do you think I have a chance at getting these apartments?

Sure why not? It doesn't really matter that you don't have rental history if you have some credit. The place I used to lease apartments at went off a point system though so it's a little hard to say. If you have any accounts in collections that could be bad but you didn't really give that impression in your question. So I don't see any reason you couldn't qualify. The places I rented (here in CA) required from 2 times the monthly rent amount in income to 3 times the monthly rent amount plus security deposit, etc. Incredible prices BTW!!!!! $590 for a 1 bedroom? Whoa. You can't get that for less than $1,300 around here. Best of luck :-)