How can I close a credit card account?

Once the actual account has been closed with the bank and you've done you have Reconciled the last statement (assuming you want/need to).

Go to your Company Chart of Accounts.  To the far right on your Credit Card Acct, use the drop down menu (black arrow) and Click on Delete. 

But don't worry, you're not actually Deleting the Acct, just making it Inactive (hiding it).  It's just a poor word choice that for some reason was never caught before QBO went live.  The expenses on the card will still show up in the appropriate reports and you can always make the account Active again if you ever need to.