LS I +61 303 is one of only a few high-mass X-ray binaries currently detected at high significance in very high energy gamma-rays. The system was observed over several orbital cycles (between September 2006 and February 2007) with the VERITAS array of imaging air-Cherenkov telescopes. A signal of gamma-rays with energies above 300 GeV is found with a statistical significance of 8.4 standard deviations. The detected flux is measured to be strongly variable; the maximum flux is found during most orbital cycles at apastron. The energy spectrum for the period of maximum emission can be characterized by a power law with a photon index of Gamma=2.40+-0.16_stat+-0.2_sys and a flux above 300 GeV corresponding to 15-20% of the flux from the Crab Nebula.
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