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Most massive galaxies are thought to have formed their dense stellar cores in early cosmic epochs. Previous studies have found galaxies with high gas velocity dispersions or small apparent sizes, 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 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 ≈ 2 (refs 8, 9, 10, 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 we infer that many star-forming cores may be heavily obscured, and could be missed in optical and near-infrared surveys. [ABSTRACT FROM AUTHOR]