  Boson stars arise as solutions of a massive complex scalar field coupled to
gravity. A variety of scalar potentials, giving rise to different types of
boson stars, have been studied in the literature. Here we study instead the
effect of promoting the kinetic term of the scalar field to a nonlinear sigma
model -- an extension that is naturally motivated by UV completions of gravity
like string theory. We consider the $\mathrm{O}(3)$ and
$\mathrm{SL}(2,\mathbb{R})$ sigma models with minimally interacting potentials
and obtain their boson star solutions. We study the maximum mass and
compactness of the solutions as a function of the curvature of the sigma model
and compare the results to the prototypical case of mini boson stars, which are
recovered in the case of vanishing curvature. The effect of the curvature turns
out to be dramatic. While $\mathrm{O}(3)$ stars are massive and can reach a
size as compact as $R\sim 3.3 GM$, $\mathrm{SL}(2,\mathbb{R})$ stars are much
more diffuse and only astrophysically viable if the bosons are ultralight.
These results show that the scalar kinetic term is at least as important as the
potential in determining the properties of boson stars.
