  We present new, fully nonlinear numerical solutions to the static,
spherically symmetric Einstein-Klein-Gordon system for a collection of an
arbitrary odd number $N$ of complex scalar fields with an internal $U(N)$
symmetry and no self-interactions. These solutions, which we dub $\ell$-boson
stars, are parametrized by an angular momentum number $\ell=(N-1)/2$, an
excitation number $n$, and a continuous parameter representing the amplitude of
the fields. They are regular at every point and possess a finite total mass.
For $\ell = 0$ the standard spherically symmetric boson stars are recovered. We
determine their generalizations for $\ell > 0$, and show that they give rise to
a large class of new static configurations which might have a much larger
compactness ratio than $\ell=0$ stars.
