Without more context, I would guess this refers to the idea of keeping a score of someone's mistakes, or faults.

In some games, such as pool, a chalkboard is available for keeping score. This idea is also used as a metaphor for keeping score when deciding if another person is someone you want to keep company with.

Often, we put one finger in the air and make a motion like marking a chalkboard, and say something like, "That's one", meaning one mark for, or against something. Another phrase sometimes used, is "Score one" (for or against). Your facial expression shows if its positive or negative.

Is it possible to "chalk disappointment up against someone"? To mean that they disappointed you and you want to remember that.

FounDit Wrote:
Yes, you can, but I'd normally say, "chalk up marks of disappointment", rather than "chalk up disappointments". You chalk up marks, and the marks would then stand for things either good or bad.

Yes, so it means here that a mark is like a point of either something bad or good.