As an exoplanet orbits its host star it reflects and emits light, forming a distinctive phase curve. By observing this light, we can study the atmosphere and surface of distant planets. The planets in our Solar System show a wide range of atmospheric phenomena, with stable wind patterns, changing storms, and evolving anomalies. Brown dwarfs also exhibit atmospheric variability. Such temporal variability in the atmosphere of a giant exoplanet has not to date been observed. HAT-P-7 b is an exoplanet with a known offset in the peak of its phase curve. Here we present variations in the peak offset ranging between -0.086+0.033-0.033 to 0.143+0.040-0.037 in phase, implying that the peak brightness repeatedly shifts from one side of the planet's substellar point to the other. The variability occurs on a timescale of tens to hundreds of days. These shifts in brightness are indicative of variability in the planet's atmosphere, and result from a changing balance of thermal emission and reflected flux from the planet's dayside. We suggest that variation in wind speed in the planetary atmosphere, leading to variable cloud coverage on the dayside and a changing energy balance, is capable of explaining the observed variation.