  We construct a cohomogeneity-1 helical black string in six-dimensional
Einstein gravity. The helical solution branches from the onset of the
gravitational superradiant instability of the equal-spinning Myers-Perry black
string. The isometry group of the helical black string is $\mathbb{R}_T \times
U(1)_Z \times SU(2)$, where the first two are helical isometries generated by
linear combinations of time translation, shifts along the string, and rotation,
each of which is individually broken by the superradiant instability. The
helical black string is stationary, non-axisymmetric, and has nonzero horizon
velocity despite the absence of momentum in the string direction. The entropy
of the helical black string is higher than that of the Myers-Perry black
string, but lower than cohomogeneity-2 ``black resonator strings'' (recently
found) when the solutions overlap in the microcanonical ensemble. The entropy
of the helical black string approaches zero when the horizon velocity along the
string reaches its maximum given by the speed of light. Nevertheless, we find
no evidence for the existence of regular horizonless solutions in this limit.
