The visible light photon counter (VLPC) is a very high quantum efficiency (QE, 88% at 694 nm) single photon detector in the visible wavelengths. The QE in the ultraviolet (UV) wavelenghths is poor in these devices due to absorption in the degenerate front contact. We introduce the ultraviolet photon counter (UVPC), where the QE in the near UV wavelength range (300-400 nm) is dramatically enhanced. The degenerate Si front contact of the VLPC is replaced with a Ti Schottky contact, which reduces the absorption of incident photons within the contact layer. We demonstrate a system QE of 5.3% at 300 nm and 11% at 370 nm for a UVPC with a Ti Schottky contact and a single layer MgF(2) antireflection coating.