Man, it's tricky when a store is closing because they will still tack on the interest after that store closes because it's through Chase and not through the actual company. And, when you close accounts with a balance, that can really hurt your credit (trust me, I know, mine is RUINED). So, I'd just pay as much as you can every month until it's paid off. And, then don't use it again. If they charge you maintenance fees or anything like that afterwards, I'd close the account.
I agree. Chase is a PITA and they will continue to go after you until you pay. So I'd also continue to pay the balance and then close the card/account when your balance is $0.
Can you transfer the balance to another card or a new card? We usually get a good rate for balance transfers. We keep an Amex Optima open for just that purpose - they're delighted to take over an existing balance. Then we pay it off without adding any new charges.