  In this paper, we will analyze a three dimensional supersymmetric
Chern-Simons theory on a manifold with a boundary. The boundary we will
consider in this paper will be defined by $n\cdot x=0$, where $n$ is a
light-like vector. It will be demonstrated that this boundary is preserved
under the action of the $SIM(1)$ subgroup of the Lorentz group. Furthermore,
the presence of this boundary will break half of the supersymmetry of the
original theory. As the original Chern-Simons theory had $\mathcal{N} =1$
supersymmetry in absence of a boundary, it will only have $\mathcal{N}=1/2$
supersymmetry in presence of this boundary. We will also observe that the
Chern-Simons theory can be made gauge invariant by introducing new degrees of
freedom on the boundary. The gauge transformation of these new degrees of
freedom will exactly cancel the boundary term obtained from the gauge
transformation of the Chern-Simons theory.
