First Talbot interferometry in the hard X-ray region was demonstrated using a pair of transmission gratings made by forming gold stripes on glass plates. By aligning the gratings on the optical axis of X-rays with a separation that caused the Talbot effect by the first grating, moiré fringes were produced inclining one grating slightly against the other around the optical axis. A phase object placed in front of the first grating was detected by moiré-fringe bending. Using the technique of phase-shifting interferometry, the differential phase corresponding to the phase object could also be measured. This result suggests that X-ray Talbot interferometry is a novel and simple method for phase-sensitive X-ray radiography.