We report the discovery of a transiting planet with an orbital period of 1.36 d orbiting the brighter component of the visual binary star BD -07 ^ { \circ } 436 . The host star , WASP-77 A , is a moderately bright G8 V star ( V=10.3 ) with a metallicity close to solar ( [ Fe/H ] = 0.0 \pm 0.1 ) . The companion star , WASP-77 B , is a K-dwarf approximately 2 magnitudes fainter at a separation of approximately 3″ . The spectrum of WASP-77 A shows emission in the cores of the Ca II H and K lines indicative of moderate chromospheric activity . The WASP lightcurves show photometric variability with a period of 15.3 days and an amplitude of about 0.3 % that is probably due to the magnetic activity of the host star . We use an analysis of the combined photometric and spectroscopic data to derive the mass and radius of the planet ( 1.76 \pm 0.06 M _ { Jup } , 1.21 \pm 0.02 R _ { Jup } ) . The age of WASP-77 A estimated from its rotation rate ( \sim 1 Gyr ) agrees with the age estimated in a similar way for WASP-77 B ( \sim 0.6 Gyr ) but is in poor agreement with the age inferred by comparing its effective temperature and density to stellar models ( \sim 8 Gyr ) . Follow-up observations of WASP-77 Ab will make a useful contribution to our understanding of the influence of binarity and host star activity on the properties of hot Jupiters .