MAGNETISM and superconductivity are manifestations of two different ordered states into which metals can condense at low temperatures. In general these states are mutually exclusive(1); they do not coexist at the same place in a sample. The study of the interplay between these properties has recently been revitalized by the discovery(2,3) of a class of compounds with formula RNi(2)B(2)C (where R is a rare-earth element) which are both antiferromagnetic and superconducting at sufficiently low temperature(4). It has been suggested(5) that magnetic and superconducting order can coexist in these materials on an atomic scale. Here we use small-angle neutron scattering to study the structure of the superconducting vortex lattice in ErNi2B2C. Our results show that the development of magnetic order causes the vortex lines to disorder and rotate away from the direction of the applied magnetic field. This coupling of superconductivity and magnetism provides clear evidence for microscopic coexistence of magnetic and superconducting order, and indicates that magnetic superconductors may exhibit a range of unusual phenomena not observed in conventional superconductors.