We present an analysis of gamma-ray data obtained with the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope in the region around 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 \pm 0.6) x 10^{-8} photons cm^{-2} s^{-1}, corresponding to a luminosity of 1.3 x 10^{34} (d/1.3 kpc)^2 erg s^{-1} in this energy range. The gamma-ray emission exhibits a possible spatial correlation with prominent Halpha filaments of 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. Reacceleration of pre-existing CRs and subsequent adiabatic compression in the filaments is sufficient to provide the required energy density of high-energy protons. Show Partial Abstract