We report the first detection of >100 MeV gamma rays associated with a behind-the-limb solar flare, which presents a unique opportunity to probe the underlying physics of high-energy flare emission and particle acceleration. On 2013 October 11 a GOES M1.5 class solar flare occurred ~ 9.9 degrees behind the solar limb as observed by STEREO-B. RHESSI observed hard X-ray emission above the limb, most likely from the flare loop-top, as the footpoints were occulted. Surprisingly, the Fermi Large Area Telescope (LAT) detected >100 MeV gamma-rays for ~30 minutes with energies up to GeV. The LAT emission centroid is consistent with the RHESSI hard X-ray source, but its uncertainty does not constrain the source to be located there. The gamma-ray spectra can be adequately described by bremsstrahlung radiation from relativistic electrons having a relatively hard power-law spectrum with a high-energy exponential cutoff, or by the decay of pions produced by accelerated protons and ions with an isotropic pitch-angle distribution and a power-law spectrum with a number index of ~3.8. We show that high optical depths rule out the gamma rays originating from the flare site and a high-corona trap model requires very unusual conditions, so a scenario in which some of the particles accelerated by the CME shock travel to the visible side of the Sun to produce the observed gamma rays may be at work.