In the course of a search for solar-like oscillations in bright late-type stars, Doppler variability was observed in the F5 subgiant Procyon. The variations have frequencies within a 1.1 mHz range centered at 0.9 mHz, and a total rms amplitude within that range of 2.5 m/s. Observations of Arcturus and scattered sunlight made with the same equipment during the same time interval show no such variation, indicating that the variations seen on Procyon are of stellar origin. The Doppler signal seen is entirely consistent with solar-like p-modes on Procyon, with maximum mode amplitudes of about 50 cm/s and periods around 20 minutes. Several statistical tests support the identification for the signal with narrow-band oscillations, but none does so conclusively. Assuming that the signal does arise from p-modes, there is evidence that the frequency splitting nu(0) is 71 micro-Hz. The data do not permit a definite estimate of this quantity, and other values of nu(0) fit the observations about equally well. In order to clarify the sources of ambiguity in this and similar observations, the data acquisition, reduction, and interpretation are described. 32 refs.