Most known terrestrial planets orbit small stars with radii less than 60 per cent of that of the Sun1,2. Theoretical models predict that these planets are more vulnerable to atmospheric loss than their counterparts orbiting Sun-like stars3,4,5,6. 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 curve7,8,9,10. 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 circulation11. 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.