Superconducting niobium films, both cylindrical and planar, have been prepared by rf sputtering in an uhv chamber which is routinely pumped to a residual pressure of 3×10−9 Torr (7.6×10−7 Pa). The superconducting transition temperature Tc of films with thicknesses greater than 2000 Å was near 9.2 K, the bulk value, while Tc decreased linearly with inverse thickness for films thinner than 1000 Å. Superconductivity was observed for the first time in Nb films thinner than 50 Å; the Tc of a 40 Å film was 4.4 K while for a 27 Å film the onset of the transition was about 2 K. Electrical continuity was maintained down to a nominal film thickness of less than 10 Å, but this film was not superconducting above 1.5 K. These results will be compared with a model which predicts the dependence of Tc on thickness.