In my experience, the anniversary points post on a statement prior to the annual fee posting; on the first card I had, it was three months prior. That would let you get the points and cancel before the fee hits. If the points and the fee post in the same statement for you, I think the fine print on the statement lets you close within a month of the fee posting and you won't owe it; you should avoid closing before any other balance is paid off. It's another matter whether this will harm your relationship with Chase, but I've closed RR cards after getting the anniversary points, and still do well with Chase cards.