Supercritical Xe at 293 K offers a Kerr nonlinearity that can exceed that of fused silica while being free of Raman scattering. It also has a much higher optical damage threshold and a transparency window that extends from the UV to the infrared. We report the observation of nonlinear phenomena, such as self-phase modulation, in hollow-core photonic crystal fiber filled with supercritical Xe. In the subcritical regime, intermodal four-wave mixing resulted in the generation of UV light in the HE12 mode. The normal dispersion of the fiber at high pressures means that spectral broadening can be clearly obtained without influence from soliton effects or material damage.