Entanglement is one of the key features of quantum information and communications technology. The method that has been used most frequently to generate highly entangled pairs of photons is parametric down-conversion. Short-wavelength entangled photons are desirable for generating further entanglement between three or four photons, but it is difficult to use parametric down-conversion to generate suitably energetic entangled photon pairs. One method that is expected to be applicable for the generation of such photons is resonant hyper-parametric scattering (RHPS): a pair of entangled photons is generated in a semiconductor via an electronically resonant third-order nonlinear optical process. Semiconductor-based sources of entangled photons would also be advantageous for practical quantum technologies, but attempts to generate entangled photons in semiconductors have not yet been successful. Here we report experimental evidence for the generation of ultraviolet entangled photon pairs by means of biexciton resonant RHPS in a single crystal of the semiconductor CuCl. We anticipate that our results will open the way to the generation of entangled photons by current injection, analogous to current-driven single photon sources.