Chappy Point 2 Chappaquiddick Rd, Edgartown, MA02539 Chappy Point is located on Chappaquiddick, which is reachable by ferry from Edgartown. The beach is located adjacent to…More the ferry, where Katama Bay and Edgartown Harbor meet. The current is very strong in this area, making the beach unsuitable for swimming. Parking is extremely limited; beachgoers are advised to park in downtown Edgartown and take the ferry to the beach. The beach is free and open to the public.