51 Pegasi, one of many nearby Sun-like stars, was undistinguished until the recent detections of apparent variations in its radial velocity, which have been attributed to reflex motion caused by a planetary companion(1,2). The velocity variation inferred from variations in the spectral lines of 51 Peg has an amplitude of 56-59 ms(-1) and a period of 4.23 days, implying a planet of at least half the mass of Jupiter moving in an embarrassingly small orbit of 0.05 astronomical units. But the techniques currently used to identify these exceedingly small radial velocity variations do not allow for the possibility that changes of comparable size might be occurring in the intrinsic shapes of the spectral lines; such variations are expected when a star pulsates or has spots on its surface, and could be mistaken for radial velocity variations. Here I present high-spectral-resolution observations of 51 Peg that show that its spectral lines exhibit intrinsic shape variations with a period of 4.23 days, and an amplitude comparable to that previously attributed(1,2) to radial velocity variations. As the presence of a planet will not influence the shapes of spectral lines, these variations are likely to reflect a hitherto unknown mode of stellar oscillation. The presence of a planet is not required to explain the data.