This Letter presents the first results from the observations of LSI +61 303 using Large Area Telescope data from the Fermi Gamma-Ray Space Telescope between 2008 August and 2009 March. Our results indicate variability that is consistent with the binary period, with the emission being modulated at 26.6 +/- 0.5 days. This constitutes the first detection of orbital periodicity in high-energy gamma rays (20 MeV-100 GeV, HE). The light curve is characterized by a broad peak after periastron, as well as a smaller peak just before apastron. The spectrum is best represented by a power law with an exponential cutoff, yielding an overall flux above 100 MeV of 0.82 +/- 0.03(stat) +/- 0.07(syst) 10^{-6} ph cm^{-2} s^{-1}, with a cutoff at 6.3 +/- 1.1(stat) +/- 0.4(syst) GeV and photon index Gamma = 2.21 +/- 0.04(stat) +/- 0.06(syst). There is no significant spectral change with orbital phase. The phase of maximum emission, close to periastron, hints at inverse Compton scattering as the main radiation mechanism. However, previous very high-energy gamma ray (>100 GeV, VHE) observations by MAGIC and VERITAS show peak emission close to apastron. This and the energy cutoff seen with Fermi suggest the link between HE and VHE gamma rays is nontrivial. Show Partial Abstract