If you don't need the cash right now hang onto it until you get your other limits up. You certainly have a chance with Chase increasing the limit. They are recon friendly. I'd also give a thought about picking up a Discover card.
If you apply for a Cap 1 unsecured card, you can likely get a rewards card with high CL from them. I suggest try the prequalifier and apply for the best one they offer.
I'd would not close it until you have 3 other major CC's. Then it is time to close it.