We report the discovery of a transiting planet with an orbital period of 1.36 days orbiting the brighter component of the visual binary star BD -07 436. 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 ± 0.1). The companion star, WASP-77 B, is a K-dwarf approximately 2 mag fainter at a separation of approximately 3″. The spectrum of WASP-77 A shows emission in the cores of the Caii H and K lines, indicative of moderate chromospheric activity. The Wide Angle Search for Planets (WASP) light curves 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 ± 0.06 MJup, 1.21 ± 0.02 RJup). The age of WASP-77 A estimated from its rotation rate (˜1 Gyr) agrees with the age estimated in a similar way for WASP-77 B (˜0.6 Gyr) but is in poor agreement with the age inferred by comparing its effective temperature and density to stellar models (˜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.Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 088.C-0011.