BICEP1 is a millimeter-wavelength telescope designed specifically to measure the inflationary B-mode polarization of the Cosmic Microwave Background (CMB) at degree angular scales. We present results from an analysis of the data acquired during three seasons of observations at the South Pole (2006 to 2008). This work extends the two-year result published in Chiang et al. (2010), with additional data from the third season and relaxed detector-selection criteria. This analysis also introduces a more comprehensive estimation of band-power window functions, improved likelihood estimation methods and a new technique for deprojecting monopole temperature-to-polarization leakage which reduces this class of systematic uncertainty to a negligible level. We present maps of temperature, E- and B-mode polarization, and their associated angular power spectra. The improvement in the map noise level and polarization spectra error bars are consistent with the 52% increase in integration time relative to Chiang et al. (2010). We confirm both self-consistency of the polarization data and consistency with the two-year results. We measure the angular power spectra at 21 <= l <= 335 and find that the EE spectrum is consistent with Lambda Cold Dark Matter (LCDM) cosmology, with the first acoustic peak of the EE spectrum now detected at 15sigma. The BB spectrum remains consistent with zero. From B-modes only, we constrain the tensor-to-scalar ratio to r = 0.03+0.27-0.23, or r < 0.70 at 95% confidence level.
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