A two-crystal X-ray interferometer for phase-contrast X-ray imaging is reported. Mechanical stability of less than 0.1 nm is required to operate the two-crystal interferometer. The feasibility of using such an interferometer at the Photon Factory using synchrotron radiation has been investigated. Interference fringes of 70% visibility were observed with 0.092 nm X-rays. This result indicates that the two-crystal X-ray interferometer can be applied to phase-contrast X-ray imaging.