The rotational states of the members in the dwarf planet-satellite systems in the trans-Neptunian region are determined by formation conditions and the tidal interaction between the components. These rotational characteristics serve as prime tracers of their evolution. A number of authors have claimed a very broad range of values for the rotation period for the dwarf planet Eris, ranging from a few hours to a rotation that is (nearly) synchronous with the orbital period (15.8 d) of its satellite, Dysnomia. In this Letter, we present new light curve data for Eris, taken with ∼1–2 m-class ground based telescopes and with the TESS and Gaia space telescopes. The TESS data did not provide a well-defined light curve period, but it could be used to constrain light curve variations to a maximum possible light curve amplitude of Δ m ≤ 0.03 mag (1- σ ) for P  ≤ 24 h periods. Both the combined ground-based data and Gaia measurements unambiguously point to a light curve period equal to the orbital period of Dysnomia, P  = 15.8 d, with a light curve amplitude of Δ m  ≈ 0.03 mag, indicating that the rotation of Eris is tidally locked. Assuming that Dysnomia has a collisional origin, calculations with a simple tidal evolution model show that Dysnomia must be relatively massive (mass ratio of q  = 0.01–0.03) and large (radius of R s  ≥ 300 km) to have the potential to slow Eris down to a synchronised rotation. These simulations also indicate that (assuming tidal parameters usually considered for trans-Neptunian objects) the density of Dysnomia should be 1.8–2.4 g cm −3 . This is an exceptionally high value among similarly sized trans-Neptunian objects, setting important constraints on their formation conditions.