Most known terrestrial planets orbit small stars with radii less than 60 per cent of that of the Sun . Theoretical models predict that these planets are more vulnerable to atmospheric loss than their counterparts orbiting Sun-like stars . To determine whether a thick atmosphere has survived on a small planet, one approach is to search for signatures of atmospheric heat redistribution in its thermal phase curve . Previous phase curve observations of the super-Earth 55 Cancri e (1.9 Earth radii) showed that its peak brightness is offset from the substellar point (latitude and longitude of 0 degrees)-possibly indicative of atmospheric circulation . Here we report a phase curve measurement for the smaller, cooler exoplanet LHS 3844b, a 1.3-Earth-radii world in an 11-hour orbit around the small nearby star LHS 3844. The observed phase variation is symmetric and has a large amplitude, implying a dayside brightness temperature of 1,040 ± 40 kelvin and a nightside temperature consistent with zero kelvin (at one standard deviation). Thick atmospheres with surface pressures above 10 bar are ruled out by the data (at three standard deviations), and less-massive atmospheres are susceptible to erosion by stellar wind. The data are well fitted by a bare-rock model with a low Bond albedo (lower than 0.2 at two standard deviations). These results support theoretical predictions that hot terrestrial planets orbiting small stars may not retain substantial atmospheres.