We present what we believe to be the first experimental demonstration of low-loss guiding of UV radiation in hollow-core photonic crystal fiber. The "kagomé" latticed fiber was designed to guide 0.355 microm wavelength radiation with approximately 2 dB/m loss. Moreover, an excellent agreement between modeling and experimental results was obtained. From this comparison it was inferred that propagation loss only arises from the lack of confinement, thereby indicating that such fibers may be designed for even shorter wavelengths where material loss prohibits the use of fused silica as a core material. As an example, a fiber was designed to be operated at 0.25 microm with 0.4 dB/m loss.