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.
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