  We consider SU(N) gauge theory in 1+1 dimensions coupled to chiral fermions
in the adjoint representation of the gauge group. With all fields in the
adjoint representation the gauge group is actually SU(N)/Z_N, which possesses
nontrivial topology. In particular, there are N distinct topological sectors
and the physical vacuum state has a structure analogous to a \theta vacuum. We
show how this feature is realized in light-front quantization for the case N=2,
using discretization as an infrared regulator. In the discretized form of the
theory the nontrivial vacuum structure is associated with the zero momentum
mode of the gauge field A^+. We find exact expressions for the degenerate
vacuum states and the analog of the \theta vacuum. The model also possess a
condensate which we calculate. We discuss the difference between this chiral
light-front theory and the theories that have previously been considered in the
equal-time approach.
