  This paper discusses the formulation of the non-commutative Chern-Simons (CS)
theory where the spatial slice, an infinite strip, is a manifold with
boundaries. As standard star products are not correct for such manifolds, the
standard non-commutative CS theory is not also appropriate here. Instead we
formulate a new finite-dimensional matrix CS model as an approximation to the
CS theory on the strip. A work which has points of contact with ours is due to
Lizzi, Vitale and Zampini where the authors obtain a description for the fuzzy
disc. The gauge fields in our approach are operators supported on a subspace of
finite dimension N+\eta of the Hilbert space of eigenstates of a simple
harmonic oscillator with N, \eta \in Z^+ and N \neq 0. This oscillator is
associated with the underlying Moyal plane. The resultant matrix CS theory has
a fuzzy edge. It becomes the required sharp edge when N and \eta goes to
infinity in a suitable sense. The non-commutative CS theory on the strip is
defined by this limiting procedure. After performing the canonical constraint
analysis of the matrix theory, we find that there are edge observables in the
theory generating a Lie algebra with properties similar to that of a
non-abelian Kac-Moody algebra. Our study shows that there are (\eta+1)^2
abelian charges (observables) given by the matrix elements (\cal A_i)_{N-1 N-1}
and (\cal A_i)_{nm} (where n or m \geq N) of the gauge fields, that obey
certain standard canonical commutation relations. In addition, the theory
contains three unique non-abelian charges, localized near the N^th level. We
show that all non-abelian edge observables except these three can be
constructed from the abelian charges above. Using the results of this analysis
we discuss the large N and \eta limit.
