Last time I was on Chesuncook was 2008, so this is dated info, but as I recall, you pay your fees at the entry gates. Not sure how you are getting there, or whether you pass through a gate. They didn't take credit cards either, and I don't know if that has changed, so you may need cash.
I'm also remembering not paying fees on the way out. That 2008 trip, we started on Moosehead, crossed the Northeast carry to the W Branch Penobscot, then finished at the point separating Chesuncook and Ripogenus. So we didn't enter through any gates and I don't think we paid fees that time. That was 15 years ago. It's probably all changed. Why don't you call North Maine Woods and ask them? Also, the Gazetteer used to be pretty good at showing camp sites and gate locations.
Perhaps some Maine locals can answer authoritatively. In '08, no gate, no pay. As I say, it's probably changed, and maybe they are like many others that want you to register and pay on line before you go.