Despite the importance of electron transfer in electrochemistry, photosynthesis, respiration, and chemical syntheses, the first-principles calculation of one-electron reduction potentials remains a significant challenge to modern computational chemistry. This contribution describes a thermodynamic cycle method, combined with hybrid Hartree-Fock-density-functional quantum chemical and thermodynamic perturbation/molecular dynamics calculations, to estimate the one-electron reduction potential for the parent of quinone electron accepters in photosynthesis and respiration, p-benzoquinone, in water at 300 K. Hybrid Hartree-Fock/density functional methods yield a calculated, gas-phase electron affinity of 1.85 eV (42.55 kcal/mol), in agreement with the experimental electron attachment free energy (42.9 kcal/mol) and thermodynamic perturbation/molecular dynamics simulations give a hydration free energy difference between p-benzoquinone and p-benzosemiquinone anion of 64.26 kcal/mol (2.79 eV). Together, the two numbers yield a computed reduction potential of 4.63 eV for p-benzoquinone, within approximately 90-100 mV of the experimental reduction potential of 4.54 eV. The exceptional accuracy attained for p-benzoquinone suggests the possible computer-aided design of molecules and their solvent or protein surroundings to achieve predictable electrochemical properties.