Alfvén waves, transverse incompressible magnetic oscillations, have been proposed as a possible mechanism to heat the Sun's corona to millions of degrees by transporting convective energy from the photosphere into the diffuse corona. We report the detection of Alfvén waves in intensity, line-of-sight velocity, and linear polarization images of the solar corona taken using the FeXIII 1074.7-nanometer coronal emission line with the Coronal Multi-Channel Polarimeter (CoMP) instrument at the National Solar Observatory, New Mexico. Ubiquitous upward propagating waves were seen, with phase speeds of 1 to 4 megameters per second and trajectories consistent with the direction of the magnetic field inferred from the linear polarization measurements. An estimate of the energy carried by the waves that we spatially resolved indicates that they are too weak to heat the solar corona; however, unresolved Alfvén waves may carry sufficient energy.