Magnetic materials can host skyrmions, which are topologically non-trivial spin textures. In chiral magnets with cubic lattice symmetry, all previously observed skyrmion phases require thermal fluctuations to become thermodynamically stable in bulk materials, and therefore exist only at relatively high temperature, close to the helimagnetic transition temperature. Other stabilization mechanisms require a lowering of the cubic crystal symmetry. Here, we report the identification of a second skyrmion phase in Cu2OSeO3 at low temperature and in the presence of an applied magnetic field. The new skyrmion phase is thermodynamically disconnected from the well-known, nearly isotropic, high-temperature phase, and exists, in contrast, when the external magnetic field is oriented along the < 100 > crystal axis only. Theoretical modelling provides evidence that the stabilization mechanism is given by well-known cubic anisotropy terms, and accounts for an additional observation of metastable helices tilted away from the applied field. The identification of two distinct skyrmion phases in the same material and the generic character of the underlying mechanism suggest a new avenue for the discovery, design and manipulation of topological spin textures.