We report the first results of a search for real photon-photon scattering using X rays. A novel system is developed to split and collide X-ray pulses by applying interferometric techniques. A total of $6.5times10^{5}$ pulses (each containing about $1
0^{11}$ photons) from an X-ray Free-Electron Laser are injected into the system. No scattered events are observed, and an upper limit of $1.7times 10^{-24}$ ${rm m^{2}}$ (95% C.L.) is obtained on the photon-photon elastic scattering cross section at 6.5 keV.
