  We numerically construct asymptotically anti-de Sitter boson star solutions
using a minimally coupled $\frac{D-1}{2}$-tuplet complex scalar field in
$D=5,7,9,11$ dimensions. The metric admits multiple Killing vector fields in
general, however the scalar fields are only invariant under a particular
combination, leading to such boson star solutions possessing just a single
helical Killing symmetry. These boson stars form a one parameter family of
solutions, which can be parametrized by the energy density at their center. As
the central energy density tends to infinity, the angular velocity, mass, and
angular momentum of the boson star exhibit damped harmonic oscillations about
finite central values, while the Kretschmann invariant diverges, signaling the
formation of a black hole in this limit.
