We demonstrate a new scheme to measure the relative arrival time between femtosecond pulses of hard X-radiation from a free electron laser and femtosecond optical pulses from an amplified laser system at the Femtosecond X-ray Experiments Instrument of European XFEL. The method is based on interference between two chirped optical pulses traversing through an X-ray stimulated diamond plate. Applying an effective medium theory we measure subtle refractive index changes of 5.7 × 10-5 due to the density of conduction band electrons generated by the sub-milli-Joule intense X-ray pulse. The setup operates with a Common-Path-Interferometer, detecting the X-ray-induced phase shift of the optical probe pulses transmitting through the diamond sample. Due to the thermal stability of the diamond sample this scheme operates well at the MHz pulse repetition rates of superconducting linac-based XFELs.