1. Astronomy Department, Yale University, 260 Whitney Avenue, New Haven, Connecticut 06511, USA
2. Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
3. Leiden Observatory, Leiden University, 2300 RA Leiden, The Netherlands

Correspondence to: Pieter G. van Dokkum¹ Correspondence and requests for materials should be addressed to P.G.v.D. (Email: pieter.vandokkum@yale.edu).

Recent studies have found that the oldest and most luminous galaxies in the early Universe are surprisingly compact^{1, 2, 3, 4, 5, 6, 7}, having stellar masses similar to present-day elliptical galaxies but much smaller sizes. This finding has attracted considerable attention^{8, 9, 10, 11, 12, 13}, as it suggests that massive galaxies have grown in size by a factor of about five over the past ten billion years (10 Gyr). A key test of these results is a determination of the stellar kinematics of one of the compact galaxies: if the sizes of these objects are as extreme as has been claimed, their stars are expected to have much higher velocities than those in present-day galaxies of the same mass. Here we report a measurement of the stellar velocity dispersion of a massive compact galaxy at redshift z = 2.186, corresponding to a look-back time of 10.7 Gyr. The velocity dispersion is very high at  km s^-1, consistent with the mass and compactness of the galaxy inferred from photometric data. This would indicate significant recent structural and dynamical evolution of massive galaxies over the past 10 Gyr. The uncertainty in the dispersion was determined from simulations that include the effects of noise and template mismatch. However, we cannot exclude the possibility that some subtle systematic effect may have influenced the analysis, given the low signal-to-noise ratio of our spectrum.