  We perturbatively construct a three-dimensional rotating AdS black hole with
a real scalar hair. We choose the mass of a scalar field slightly above the
Breitenlohner-Freedman bound and impose a more general boundary condition for
the bulk scalar field at AdS infinity. We first show that rotating BTZ black
holes are unstable against superradiant modes under our more general boundary
condition. Next we construct a rotating hairy black hole perturbatively with
respect to a small amplitude $\epsilon$ of the scalar field, up to
$O(\epsilon^4)$. The lumps of non-linearly perturbed geometry admit only one
Killing vector field and co-rotate with the black hole, and it shows no
dissipation. We numerically show that the entropy of our hairy black hole is
larger than that of the BTZ black hole with the same energy and the angular
momentum. This indicates, at least in the perturbative level, that our rotating
hairy black hole in lumpy geometry can be the endpoint of the superradiant
instability.
