We report on the gamma-ray observations of giant molecular clouds Orion A and B with the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. The gamma-ray emission in the energy band between approx 100 MeV and approx 100 GeV is predicted to trace the gas mass distribution in the clouds through nuclear interactions between the Galactic cosmic rays (CRs) and interstellar gas. The gamma-ray production cross-section for the nuclear interaction is known to approx 10% precision which makes the LAT a powerful tool to measure the gas mass column density distribution of molecular clouds for a known CR intensity. We present here such distributions for Orion A and B, and correlate them with those of the velocity-integrated CO intensity (W(sub CO)) at a 1 deg 1 deg pixel level. The correlation is found to be linear over a W(sub CO) range of approx 10-fold when divided in three regions, suggesting penetration of nuclear CRs to most of the cloud volumes. The W(sub CO)-to-mass conversion factor, X(sub CO), is found to be approx 2.3 10(exp 20) / sq cm (K km/s)(exp -1) for the high-longitude part of Orion A (l > 212 deg), approx 1.7 times higher than approx 1.3 10(exp 20) found for the rest of Orion A and B. We interpret the apparent high X(sub CO) in the high-longitude region of Orion A in the light of recent works proposing a nonlinear relation between H2 and CO densities in the diffuse molecular gas.W(sub CO) decreases faster than the H2 column density in the region making the gas "darker" to W(sub CO)
