XeF doped solid Kr represents a novel solid state exciplex laser. A net gain in excess of 100 cm-1 and a superradiant beam of 5 mrad divergence are observed over the XeF(D --> X) transition at 301 nm, when free standing crystals of XeF doped Kr are optically pumped near the XeF(D <-- X) absorption maximum at 260 nm. Superlinear dependence of gain on pump intensity and low divergence of the amplified beam are taken as evidence for self-focusing. The XeF (D) state is effectively isolated from the lower manifold of charge transfer states in solid Kr, which includes XeF(B,C) and (KrXe) +F-.