We report the discovery and confirmation of a transiting circumbinary planet (PH1b) around KIC 4862625, an eclipsing binary in the Kepler field. The planet was discovered by volunteers searching the first six Quarters of publicly available Kepler data as part of the Planet Hunters citizen science project. Transits of the planet across the larger and brighter of the eclipsing stars are detectable by visual inspection every similar to 137 days, with seven transits identified in Quarters 1-11. The physical and orbital parameters of both the host stars and planet were obtained via a photometric-dynamical model, simultaneously fitting both the measured radial velocities and the Kepler light curve of KIC 4862625. The 6.18 +/- 0.17 R-circle plus planet orbits outside the 20 day orbit of an eclipsing binary consisting of an F dwarf (1.734 +/- 0.044 R-circle dot, 1.528 +/- 0.087 M-circle dot) and M dwarf (0.378 +/- 0.023 R-circle dot, 0.408 +/- 0.024 M-circle dot). For the planet, we find an upper mass limit of 169 M-circle plus (0.531 Jupiter masses) at the 99.7% confidence level. With a radius and mass less than that of Jupiter, PH1b is well within the planetary regime. Outside the planet's orbit, at similar to 1000 AU, a previously unknown visual binary has been identified that is likely bound to the planetary system, making this the first known case of a quadruple star system with a transiting planet.