This Letter presents the first results from the observations of LSI +61 303 ( catalog LS~I~+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 \pm 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 \pm 0.03 ( stat ) \pm 0.07 ( syst ) 10 ^ { -6 } ph cm ^ { -2 } s ^ { -1 } , with a cutoff at 6.3 \pm 1.1 ( stat ) \pm 0.4 ( syst ) GeV and photon index \Gamma = 2.21 \pm 0.04 ( stat ) \pm 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 .