Resonant inelastic X-ray scattering and X-ray emission spectroscopy can be used to probe the energy and dispersion of the elementary low-energy excitations that govern functionality in matter: vibronic, charge, spin and orbital excitations(1-7). A key drawback of resonant inelastic X-ray scattering has been the need for high photon densities to compensate for fluorescence yields of less than a per cent for soft X-rays(8). Sample damage from the dominant non-radiative decays thus limits the materials to which such techniques can be applied and the spectral resolution that can be obtained. A means of improving the yield is therefore highly desirable. Here we demonstrate stimulated X-ray emission for crystalline silicon at photon densities that are easily achievable with free-electron lasers(9). The stimulated radiative decay of core excited species at the expense of non-radiative processes reduces sample damage and permits narrow-bandwidth detection in the directed beam of stimulated radiation. We deduce how stimulated X-ray emission can be enhanced by several orders of magnitude to provide, with high yield and reduced sample damage, a superior probe for low-energy excitations and their dispersion in matter. This is the first step to bringing nonlinear X-ray physics in the condensed phase from theory(10-16) to application.