  We study a matrix model describing type IIB superstring in orbifold
backgrounds. We particularly consider a {\bf C}^3/{\bf Z}_3 orbifold model
whose six dimensional transverse space is orbifolded by {\bf Z}_3 discrete
symmetry. This model is chiral and has d=4 {\cal N}=1 supersymmetry of
Yang-Mills type as well as an inhomogeneous supersymmetry specific to matrix
models. We calculate one-loop effective action around some backgrounds, and the
result can be interpreted as interactions mediated by massless particles in IIB
supergravity in orbifold background, if the background is in the Higgs branch.
If the background is in the Coulomb branch, the dynamics is governed by the
reduced model of d=4 super Yang-Mills theory, which might be interpreted as
exchange of massless particles in the twisted sector. But the perturbative
calculation cannot reproduce the supergravity result. We also show that this
model with a large Higgs vacuum expectation value becomes IIB (IKKT) matrix
model.
