We report the discovery by the CoRoT  space mission of a new giant planet , CoRoT-20b . The planet has a mass of 4.24 \pm 0.23 M _ { Jup }  and a radius of 0.84 \pm 0.04 R _ { Jup } . With a mean density of 8.87 \pm 1.10 g cm ^ { -3 } , it is among the most compact planets known so far . Evolution models for the planet suggest a mass of heavy elements of the order of 800 M _ { \oplus } if embedded in a central core , requiring a revision either of the planet formation models or of planet evolution and structure models . We note however that smaller amounts of heavy elements are expected from more realistic models in which they are mixed throughout the envelope . The planet orbits a G-type star with an orbital period of 9.24 days and an eccentricity of 0.56 . The star ’ s projected rotational velocity is v sin i  = 4.5 \pm 1.0 km s ^ { -1 } , corresponding to a spin period of 11.5 \pm 3.1 days if its axis of rotation is perpendicular to the orbital plane . In the framework of Darwinian theories and neglecting stellar magnetic breaking , we calculate the tidal evolution of the system and show that CoRoT-20b  is presently one of the very few Darwin-stable planets that is evolving towards a triple synchronous state with equality of the orbital , planetary and stellar spin periods .