A new scheme of X-ray pump-probe experiment is suggested in this Letter, namely resonant inelastic X-ray scattering accompanied by core-hole hopping induced by a strong laser field. In particular, we study the dynamics of X-ray Raman scattering of N-2 molecules in a strong IR field. The laser-induced mixing of the core holes of opposite parities opens symmetry forbidden scattering channels. The strength of the symmetry forbidden channels strongly depends on the interrelationship between the time of Rabi flopping of the core holes and the scattering duration or the duration of the X-ray pulse. (C) 2008 Elsevier B.V. All rights reserved.