PKS 2131−021 is a blazar that shows peculiar variability in the radio light curve: within 45 years of recorded data, two epochs show strong sinusoidal variation with roughly the same period and phase, straddling a 20 year period when this variation was absent. Our statistical analyses demonstrate conclusively, at the 4.6σ significance level, that the periodicity in this object is not due to random fluctuations in flux density. A simple model can explain the sinusoidal variability as a result of modulated Doppler boosting due to the orbital motion of a supermassive black hole binary. The observed period suggests an orbital separation of ∼0.001–0.01 pc. If sufficiently massive, this system may produce gravitational waves detectable with future pulsar timing arrays.