Ask HN: Are hours spent dealing with billing, billable?

I have a client who recently refused to pay a very large bill on time and was 60 days late. It took me 3 hours total of emails, phone calls, etc. to get him to arrive at a payment plan.

Then I went and billed him for 1 of those hours. He doesn't want to pay that hour. I did it half to get some pay back on my time, half to stick it to him. Do I have any grounds for this or should I just drop the hour?