  We construct asymptotically anti-de Sitter boson stars in
Einstein-Gauss-Bonnet gravity coupled to a $\frac{D-1}{2}$-tuplet of complex
massless scalar fields both perturbatively and numerically in D=5,7,9,11
dimensions. These solutions possess just a single helical Killing symmetry due
to the choice of scalar fields. The energy density at the centre of the star
characterizes the solutions, and for each choice of the Gauss-Bonnet coupling
$\alpha$ we obtain a one parameter family of solutions. All solutions respect
the first law of thermodynamics; in the numerical case to within 1 part in
$10^6$. We describe the dependence of the angular velocity, mass, and angular
momentum of the boson stars on $\alpha$ and on the dimensionality. For D>5,
these quantities exhibit damped oscillations about finite central values as the
central energy density tends to infinity, where the amplitude of oscillation
increases nonlinearly with $\alpha$. In the limit of diverging central energy
density, the Kretschmann invariant at the centre of the boson star also
diverges. This is in contrast to the D=5 case, where the Kretschmann invariant
diverges at a finite value of the central energy density.
