  The black hole entropy calculation for type I isolated horizons, based on
loop quantum gravity, is extended to include non-minimally coupled scalar
fields. Although the non-minimal coupling significantly modifies quantum
geometry, the highly non-trivial consistency checks for the emergence of a
coherent description of the quantum horizon continue to be met. The resulting
expression of black hole entropy now depends also on the scalar field precisely
in the fashion predicted by the first law in the classical theory (with the
same value of the Barbero-Immirzi parameter as in the case of minimal
coupling).
