Internal water molecules in proteins are conceivably part of the protein structure, not exchanging easily with the bulk. We present a detailed molecular dynamics study of the water molecule bound to the green fluorescent protein (GFP) chromophore that conducts its proton following photoexcitation. It readily exchanges above 310 K through a hole that forms between strands 7 and 10, due to fluctuations in the 6-7 loop. As the hole widens, rapid succession of water exchange events occur. The exiting water molecule passes three layers of atoms, constituting the binding, internal, and surface sites. Along this pathway, hydrogen bonding protein residues are replaced with water molecules. The mean squared displacement along this pathway is initially subdiffusive, becomes superdiffusive as the water traverses the protein wall in a flip-flop motion, and reverts to normal diffusion in the bulk. The residence correlation function for the bound state decays biexponentially, supporting this three-site scenario. For a favorable orientation of the Thr203 side-chain, the hole often fills with a single file of water molecules that could indeed rapidly conduct the photodissociated proton outside the protein. The activation enthalpy for its formation, 26 kJ/mol, agrees with the experimental value for a protein conformation change suggested to gate proton escape.