  We consider a gravitating spherically symmetric configuration consisting of a
scalar field non-minimally coupled to ordinary matter in the form of a perfect
fluid. For this system we find static, regular, asymptotically flat solutions
for both relativistic and non-relativistic cases. It is shown that the presence
of the non-minimal interaction leads to substantial changes both in the radial
matter distribution of the star and in the star's total mass. A simple
stability test indicates that, for the choice of parameters used in the paper,
the solutions are unstable.
