They probably don't want to advise people on whether or not to close the cards. I did tons of Chase bonuses in the past (for the cash bonuses, not travel, but should work the same) and I always closed the card before the annual fee hit. If you have another Chase card open, you shouldn't lose points because they are all banked in one account. Another option is to ask them to downgrade your card to one of the non-annual fee options (the regular Chase Sapphire, for example) and that should also allow you to keep your points. Not sure if downgrading your card counts as one of the 5/24 though....Chase might have to answer that.