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We present the results of observations of the TeV binary LS I + 61 degrees 303 with the VERITAS telescope array between 2008 and 2010, at energies above 300 GeV. In the past, both ground-based gamma-ray telescopes VERITAS and MAGIC have reported detections of TeV emission near the apastron phases of the binary orbit. The observations presented here show no strong evidence for TeV emission during these orbital phases; however, during observations taken in late 2010, significant emission was detected from the source close to the phase of superior conjunction (much closer to periastron passage) at a 5.6 standard deviation (5.6 sigma) post-trials significance. In total, between 2008 October and 2010 December a total exposure of 64.5 hr was accumulated with VERITAS on LS I + 61 degrees 303, resulting in an excess at the 3.3 sigma significance level for constant emission over the entire integrated data set. The flux upper limits derived for emission during the previously reliably active TeV phases (i.e., close to apastron) are less than 5% of the Crab Nebula flux in the same energy range. This result stands in apparent contrast to previous observations by both MAGIC and VERITAS which detected the source during these phases at 10% of the Crab Nebula flux. During the two year span of observations, a large amount of X-ray data were also accrued on LS I + 61 degrees 303 by the Swift X-ray Telescope and the Rossi X-ray Timing Explorer Proportional Counter Array. We find no evidence for a correlation between emission in the X-ray and TeV regimes during 20 directly overlapping observations. We also comment on data obtained contemporaneously by the Fermi Large Area Telescope.