  The Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) comprises deep
multi-colour (u*g'r'i'z') photometry spanning 154 square degrees, with accurate
photometric redshifts and shape measurements. We demonstrate that the redshift
probability distribution function summed over galaxies provides an accurate
representation of the galaxy redshift distribution accounting for random and
catastrophic errors for galaxies with best fitting photometric redshifts z_p <
1.3.
  We present cosmological constraints using tomographic weak gravitational
lensing by large-scale structure. We use two broad redshift bins 0.5 < z_p <=
0.85 and 0.85 < z_p <= 1.3 free of intrinsic alignment contamination, and
measure the shear correlation function on angular scales in the range ~1-40
arcmin. We show that the problematic redshift scaling of the shear signal,
found in previous CFHTLS data analyses, does not afflict the CFHTLenS data. For
a flat Lambda-CDM model and a fixed matter density Omega_m=0.27, we find the
normalisation of the matter power spectrum sigma_8=0.771 \pm 0.041. When
combined with cosmic microwave background data (WMAP7), baryon acoustic
oscillation data (BOSS), and a prior on the Hubble constant from the HST
distance ladder, we find that CFHTLenS improves the precision of the fully
marginalised parameter estimates by an average factor of 1.5-2. Combining our
results with the above cosmological probes, we find Omega_m=0.2762 \pm 0.0074
and sigma_8=0.802 \pm 0.013.
