IN 1930 Eddington suggested1 that pulsations in stars, particularly in Cepheid variables, might be due to a feedback between core temperature and nuclear energy generation rate, which he called the ∊ -mechanism. However, Cepheid pulsation, with a typical period of a few days, is now known to be due to a feedback between temperature and opacity, the κ-mechanism2. It has been suggested that Wolf-Rayet stars, the stripped cores of highly evolved stars, might be susceptible to instability by the ∊ -mechanism on a characteristic timescale of tens of minutes3-7, and that this instability might drive powerful stellar winds which could be responsible for huge mass-loss; Wolf-Rayet stars with initial masses of >30 Msolar nearly evaporate in their entirety8. Here we report the detection of a 627-second periodicity in the WN8 star HD96548 (also known as WR40; ref. 9). Over an observing period of 150 minutes a peak-to-peak variation of 0.005 magnitude was established, and there is some evidence of a first overtone. Theoretical models of WR structure indicate that this periodicity is consistent with the fundamental radial mode, and that it could be partly driven by the ∊-mechanism.