Quasars have long been known to be variable sources at all wavelengths . Their optical variability is stochastic , can be due to a variety of physical mechanisms , and is well-described statistically in terms of a damped random walk model [ ] . The recent availability of large collections of astronomical time series of flux measurements ( light curves ) [ ] offers new data sets for a systematic exploration of quasar variability . Here we report on the detection of a strong , smooth periodic signal in the optical variability of the quasar PG 1302-102 with a mean observed period of 1,884 \pm 88 days . It was identified in a search for periodic variability in a data set of light curves for 247,000 known , spectroscopically confirmed quasars with a temporal baseline of \sim 9 years . While the interpretation of this phenomenon is still uncertain , the most plausible mechanisms involve a binary system of two supermassive black holes with a subparsec separation . Such systems are an expected consequence of galaxy mergers and can provide important constraints on models of galaxy formation and evolution .