We report the discovery of WASP-3b, the third transiting exoplanet to be discovered by the WASP and SOPHIE collaboration. WASP-3b transits its host star USNO-B1.0 1256-0285133 every 1.846834+-0.000002 days. Our high precision radial-velocity measurements present a variation with amplitude characteristic of a planetary-mass companion and in-phase with the light-curve. Adaptive optics imaging shows no evidence for nearby stellar companions, and line-bisector analysis excludes faint, unresolved binarity and stellar activity as the cause of the radial-velocity variations. We make a preliminary spectroscopic analysis of the host star finding it to have Teff = 6400+-100 K and log g = 4.25+-0.05 which suggests it is most likely an unevolved main sequence star of spectral type F7-8V. Our simultaneous modelling of the transit photometry and reflex motion of the host leads us to derive a mass of 1.76 +0.08 -0.14 M_J and radius 1.31 +0.07-0.14 R_J for WASP-3b. The proximity and relative temperature of the host star suggests that WASP-3b is one of the hottest exoplanets known, and thus has the potential to place stringent constraints on exoplanet atmospheric models.