  Neutron diffraction has been used to determine the magnetic structure of
Na$_8$Cu$_5$O$_{10}$, a stoichiometric compound containing chains based on
edge-sharing CuO$_4$ 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 $T_N = 23$ 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.
