  Neutron diffraction and bulk measurements are used to determine the nature of
the low-temperature ordered state in LiCu$_2$O$_2$, a $S=1/2$ spin-chain
compound with competing interactions. The magnetic structure is found to be
helimagnetic, with a propagation vector $(0.5,\zeta,0)$, $\zeta=0.174$. The
nearest-neighbor exchange constant and frustration ratio are estimated to be
$J=5.8$ meV and $J_2/J_1=0.29$, respectively. For idealized spin chains these
parameter values would signify a gapped spin-liquid ground state. Long-range
ordering is attributed to intrinsic non-stoichiometry.
