Solar cells based on organometallic halide perovskite absorber layers are emerging as a high-performance photovoltaic technology. Using highly sensitive photothermal deflection and photocurrent spectroscopy, we measure the absorption spectrum of CH3NH3PbI3 perovskite thin films at room temperature. We find a high absorption coefficient with particularly sharp onset. Below the bandgap, the absorption is exponential over more than four decades with an Urbach energy as small as 15 meV, which suggests a well-ordered microstructure. No deep states are found down to the detection limit of similar to 1 cm(-1). These results confirm the excellent electronic properties of perovskite thin films, enabling the very high open-circuit voltages reported for perovskite solar cells. Following intentional moisture ingress, we find that the absorption at photon energies below 2.4 eV is strongly reduced, pointing to a compositional change of the material.