  In this paper, we will analyse a three dimensional supersymmetric
Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz
symmetry down to the SIM(1) symmetry, breaks half the supersymmetry of the
Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant
Chern-Simons theory with N=1 supersymmetry will break down to N=1/2
supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry.
First, we will write the Chern-Simons action using SIM(1) projections of N=1
superfields. However, as the SIM(1) transformations of these projections are
very complicated, we will define SIM(1) superfields which transform simply
under SIM(1) transformations. We will then express the Chern-Simons action
using these SIM(1) superfields. Furthermore, we will analyse the gauge symmetry
of this Chern-Simons theory. This is the first time that a Chern-Simons theory
with N=1/2 supersymmetry will be constructed on a manifold without a boundary.
