We present an analysis of gamma-ray data obtained with the Large Area Telescope on board the Fermi Gamma-ray Space Telescope in the region around supernova remnant (SNR) S147 (G180.0-1.7). A spatially extended gamma-ray source detected in an energy range of 0.2-10 GeV is found to coincide with SNR S147. We confirm its spatial extension at >5sigma confidence level. The gamma-ray flux is (3.8 + or - 0.6) x 10 super(-8) photons cm super(-2) s super(-1), corresponding to a luminosity of 1.3 x 10 super(34) (d/1.3 kpc) super(2) erg s super(-1) in this energy range. The gamma-ray emission exhibits a possible spatial correlation with the prominent H alpha filaments of SNR S147. There is no indication that the gamma-ray emission comes from the associated pulsar PSR J0538 + 2817. The gamma-ray spectrum integrated over the remnant is likely dominated by the decay of neutral pi mesons produced through the proton-proton collisions in the filaments. The reacceleration of the pre-existing cosmic rays and subsequent adiabatic compression in the filaments is sufficient to provide the energy density required of high-energy protons.