Neutron diffraction has been used to determine the magnetic structure of Na8Cu5O10, a stoichiometric compound containing chains based on edge-sharing CuO4 plaquettes. The chains are doped with 2/5 hole per Cu site and exhibit long-range commensurate charge order with an onset well above room temperature. Below TN=23 K, the neutron data indicate long-range collinear magnetic order with a spin-density modulation whose propagation vector is commensurate along, and incommensurate perpendicular to, the chains. Competing interchain exchange interactions are discussed as a possible origin of the incommensurate magnetic order.