  We report susceptibility, specific heat, and neutron diffraction measurements
on NaCu$_2$O$_2$, a spin-1/2 chain compound isostructural to LiCu$_2$O$_2$,
which has been extensively investigated. Below 13 K, we find a long-range
ordered, incommensurate magnetic helix state with a propagation vector similar
to that of LiCu$_2$O$_2$. In contrast to the Li analogue, substitutional
disorder is negligible in NaCu$_2$O$_2$. We can thus rule out that the helix is
induced by impurities, as was claimed on the basis of prior work on
LiCu$_2$O$_2$. A spin Hamiltonian with frustrated longer-range exchange
interactions provides a good description of both the ordered state and the
paramagnetic susceptibility.
