I think each cc company has thier own policy wheter or not you can close an account with a balance. One thing I know for sure is that you don't want to have a closed cc account with a balance. It definitely hurts your score as related to utilization..
(You can however still pay over time)
At least that was my experience.
I'd advise to keep it open and pay as much as you can. When it's a 0 balance, then close it if you really want to, but unless there are crazy fees or an annual fee, you probably should just keep it open..
Rust never sleeps and neither does my fico score...