Using a first-principles density-functional method, we have calculated the single-chain band structure for the alpha-helical protein polyglycine as a function of proton position along the N ... H ... O hydrogen bond. Calculations have been carried out using both the local-density approximation (LDA) and the Perdew-Wang generalized gradient approximation (GGA) for the exchange-correlation potential. We present results for the total energy, band structure, charge densities, and Mulliken charges as a function of proton position. The total energy gives an asymmetric double-well potential for simultaneous proton shift, with the global minimum (at a N-H distance of 0.95 Angstrom) 2.02 eV (46.6 kcal/mol) below the top of the barrier with the GGA, and 1.83 eV (42.2 kcal/mol) below with the LDA.