  We construct a gauge theory on a noncommutative homogeneous K\"ahler
manifold, where we employ the deformation quantization with separation of
variables for K\"ahler manifolds formulated by Karabegov. A key point in this
construction is to obtaining vector fields which act as inner derivations for
the deformation quantization. We show that these vector fields are the only
Killing vector fields. We give an explicit construction of this gauge theory on
noncommutative ${\mathbb C}P^N$ and noncommutative ${\mathbb C}H^N$.
