Most massive galaxies are thought to have formed their dense stellar cores in early cosmic epochs(1-3). Previous studies have found galaxies with high gas velocity dispersions(4) or small apparent sizes(5-7), but so far no objects have been identified with both the stellar structure and the gas dynamics of a forming core. Here we report a candidate core in the process of formation 11 billion years ago, at redshift z = 2.3. This galaxy, GOODS-N-774, has a stellar mass of 100 billion solar masses, a half-light radius of 1.0 kiloparsecs and a star formation rate of 90(-20)(+45) solar masses per year. The star-forming gas has a velocity dispersion of 317 +/- 30 kilometres per second. This is similar to the stellar velocity dispersions of the putative descendants of GOODS-N-774, which are compact quiescent galaxies at z approximate to 2 (refs 8-11) and giant elliptical galaxies in the nearby Universe. Galaxies such as GOODS-N-774 seem to be rare; however, from the star formation rate and size of this galaxy weinfer that many star-forming cores may be heavily obscured, and could be missed in optical and near-infrared surveys.