We present the resonant inelastic X-ray scattering (RIXS) spectra of BeO at the Be 1s photoabsorption edge. The RIXS spectra excited in the vicinity of the core exciton resonance show two principal features: the scattering on a valence exciton (which at higher excitation energies verges into the characteristic K␣ emission), and a remarkably strong energy loss side-band to the elastic scattering peak, which has a maximum width of 6 eV and has intensity, at resonance, comparable to the valence scattering. The energy loss side-band appears to result from rapid lattice relaxation at the absorption site on the X-ray scattering time-span.