I know Chase does not offer secured credit card right now. I went to Chase bank and asked the rep already.
You should try Bank of America secured CC or US BankCorp. I think it's easier to get a secured card if you have a checking or saving acct with that bank, but I think you don't have to open a checking acct with them to get one.
Liked me, I have been banking with Bank of America for 5 years. They know everything about me (good customer), so they offer me a partial secured card. It means I have to give them $100, then they give me a secured card for $500 credit limit (plus $39 for annual fees). After one year of using that card with good payments, balances, scores... They promise to give my deposit money back ($100 plus interest), and they also offer me a unsecured credit card.
I'm very new liked you, I just had their secured card for 4 months. Go try with BofA, I know they will give you one