About half of the satellites in the Andromeda galaxy (M 31), all with the same sense of rotation about their host, form a planar subgroup that is extremely wide but also very thin. Giant spiral galaxies are assembled from smaller systems through a process known as hierarchical clustering. In orbit around these giants are dwarf galaxies, which are presumably remnants of the galactic progenitors. Recent studies of the dwarf galaxies of the Milky Way have led some astronomers to suspect that their orbits are not randomly distributed. This suspicion, which challenges current theories of galaxy formation, is now bolstered by the discovery of a plane of dwarf galaxies corotating as a coherent pancake-like structure around the Andromeda galaxy, the Milky Way's close neighbour and in many respects its 'twin'. The structure is extremely thin yet contains about half of the dwarf galaxies in the Andromeda system. The authors report that 13 of the 15 satellites in the plane share the same sense of rotation. Dwarf satellite galaxies are thought to be the remnants of the population of primordial structures that coalesced to form giant galaxies like the Milky Way1. It has previously been suspected2 that dwarf galaxies may not be isotropically distributed around our Galaxy, because several are correlated with streams of H i emission, and may form coplanar groups3. These suspicions are supported by recent analyses4,5,6,7. It has been claimed7 that the apparently planar distribution of satellites is not predicted within standard cosmology8, and cannot simply represent a memory of past coherent accretion. However, other studies dispute this conclusion9,10,11. Here we report the existence of a planar subgroup of satellites in the Andromeda galaxy (M 31), comprising about half of the population. The structure is at least 400 kiloparsecs in diameter, but also extremely thin, with a perpendicular scatter of less than 14.1 kiloparsecs. Radial velocity measurements12,13,14,15 reveal that the satellites in this structure have the same sense of rotation about their host. This shows conclusively that substantial numbers of dwarf satellite galaxies share the same dynamical orbital properties and direction of angular momentum. Intriguingly, the plane we identify is approximately aligned with the pole of the Milky Way’s disk and with the vector between the Milky Way and Andromeda.