  We show that models of the Dirac gaugino can naturally be embedded into a
kind of the grand unified theory (GUT), the grand gauge-Higgs unification
(gGHU) model, with the gauge group SU(5)\times SU(5)/Z_2 on an S^1/Z_2
orbifold. The supersymmetric gGHU is known to posess a light chiral adjoint
supermultiplet after the GUT breaking, thank to the exchange symmetry of two
SU(5) groups. Identifying the `predicted' adjoint fermion with the Dirac
partner of the gaugino, we argue that the supersoft term, responsible for the
Dirac gaugino mass, can be obtained from the supersymmetric Chern-Simons (CS)
like term in the gGHU setup. Although the latter term does not respect the
exchange symmetry, we propose a novel way to introduce its breaking effect
within a consistent orbifold construction. We also give a concrete setup of
fermion field contents (bulk and boundary-localized fermions) that induce the
requisite CS-like term, and calculate its coefficient from the bulk profile of
chiral fermion zero modes. Our gGHU setup may be regarded as an
extra-dimensional realization of the Goldstone gaugino scenario that was
proposed before as a solution to the problem of the adjoint scalar masses.
