  We construct D-branes in a left-right asymmetrically gauged WZW model, with
the gauge subgroup embedded differently on the left and the right of the group
element. The symmetry-preserving boundary conditions for the group-valued field
$g$ are described, and the corresponding action is found. When the subgroup
$H=U(1)$, we can implement T-duality on the axially gauged WZW action; an
orbifold of the vectorially gauged theory is produced. For the parafermion
$SU(2)/U(1)$ coset model, a $\sigma$-model is obtained with vanishing gauge
field on D-branes. We show that a boundary condition surviving from the SU(2)
parent theory characterizes D-branes in the parafermion theory, determining the
shape of A-branes. The gauge field on B-branes is obtained from the boundary
condition for A-branes, by the orbifold construction and T-duality. These gauge
fields stabilize the B-branes.
