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 2006 September and 2007 February) with the VERITAS array of imaging air Cerenkov 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.