Either way will cost you a hard inquiry as Chase does a hard pull or CLI. I would search on this site for BK friendly bank cards if you need a new card. Additional tradelines in good standing are always a good thing.
I'd apply for another card. It's nice to have a back-up in case your card is compromised and you need a new account number or if they screw up and apply your payment incorrectly and you don't have enough credit left for your purchase, etc. I know these things are pretty rare but they can be a hassle.
But like the other poster mentioned, if you go that route look for someone BK-friendly so you don't rack up inquiries for nothing.
ilovepizza is, as is often the case, right on the money. If you only have one CC, that looks awfully thin to the FICO formulas. For optimum credit you really should have at least four revolving accounts. This is especially true if you're trying to dilute the effects of a previous baddie like a BK.
- - - - in a credit-scoring postnuclear Stone Age...