We were just at HH last week. Here is the beach chair scoop:
You rent them at the beach from a company that does all the rentals on all the beaches at HHI. When I got there the first day, all the ones that were set up were taken. I had to wait about 1/2 hour, and they had retrieved more and we got ours. We rented 2 chairs and an umbrella. Reserve for all your days at once because pricing decreases after the first day. The first day, the 2 ch/umbrella were $28, then $17 per day after that (but only if you reserve/pay up front). I wish we would have rented for the entire 5 days at once. Partial day rentals were not an option. We charged them on our Disney room key. Enjoy!