We present a finely binned tomographic weak lensing analysis of the Canada-France-Hawaii Telescope Lensing Survey ({CFHTLenS)} mitigating contamination to the signal from the presence of intrinsic galaxy alignments via the simultaneous fit of a cosmological model and an intrinsic alignment model. {CFHTLenS} spans 154 square degrees in five optical bands, with accurate shear and photometric redshifts for a galaxy sample with a median redshift of zm = 0.70. We estimate the 21 sets of cosmic shear correlation functions associated with six redshift bins, each spanning the angular range of 1.5 {\textless} ?? {\textless} 35 arcmin. We combine this {CFHTLenS} data with auxiliary cosmological probes: the cosmic microwave background with data from {WMAP7}, baryon acoustic oscillations with data from Baryon Oscillation Spectroscopic Survey and a prior on the Hubble constant from the Hubble Space Telescope distance ladder. This leads to constraints on the normalization of the matter power spectrum ??8 = 0.799 ?? 0.015 and the matter density parameter ??m = 0.271 ?? 0.010 for a flat ?? cold dark matter ({??CDM)} cosmology. For a flat {wCDM} cosmology, we constrain the dark energy equation-of-state parameter w = -1.02 ?? 0.09. We also provide constraints for curved {??CDM} and {wCDM} cosmologies. We find the intrinsic alignment contamination to be galaxy-type dependent with a significant intrinsic alignment signal found for early-type galaxies, in contrast to the late-type galaxy sample for which the intrinsic alignment signal is found to be consistent with zero.