  We consider static, spherically symmetric equilibrium configurations
consisting of fermionic dark matter nonminimally coupled to dark energy in the
form of a quintessence scalar field. With the scalar field coupling function,
the form of which is taken to meet cosmological observations, we estimate the
effect of such a nonminimal coupling on the properties of dark matter compact
configurations. We show that the masses and sizes of the resulting chameleon
dark matter stars are smaller than those of systems with no field present.
