Context : The CoRoT  space mission routinely provides high-precision photometric measurements of thousands of stars that have been continuously observed for months . Aims : The discovery and characterization of the first very massive transiting planetary companion with a short orbital period is reported . Methods : A series of 34 transits was detected in the CoRoT  light curve of an F3V star , observed from May to October 2007 for 152 days . The radius was accurately determined and the mass derived for this new transiting , thanks to the combined analysis of the light curve and complementary ground-based observations : high-precision radial-velocity measurements , on-off photometry , and high signal-to-noise spectroscopic observations . Results : CoRoT-Exo-3b has a radius of 1.01 \pm 0.07 R _ { Jup }  and transits around its F3-type primary every 4.26 days in a synchronous orbit . Its mass of 21.66 \pm 1.0 M _ { Jup } , density of 26.4 \pm 5.6 g cm ^ { -3 } , and surface gravity of \log g = 4.72 clearly distinguish it from the regular close-in planet population , making it the most intriguing transiting substellar object discovered so far . Conclusions : With the current data , the nature of CoRoT-Exo-3b is ambiguous , as it could either be a low-mass brown-dwarf or a member of a new class of “ superplanets ” . Its discovery may help constrain the evolution of close-in planets and brown-dwarfs better . Finally , CoRoT-Exo-3b confirms the trend that massive transiting giant planets ( M \geq 4 M _ { Jup } ) are found preferentially around more massive stars than the Sun .