  We study the effects of addition of Chern-Simons (CS) term in the minimal
Yang Mills (YM) matrix model composed of two $2 \times 2$ matrices with $SU(2)$
gauge and $SO(2)$ global symmetry. We obtain the Hamiltonian of this system in
appropriate coordinates and demonstrate that its dynamics is sensitive to the
values of both the CS coupling, $\kappa$, and the conserved conjugate momentum,
$p_\phi$, associated to the $SO(2)$ symmetry. We examine the behavior of the
emerging chaotic dynamics by computing the Lyapunov exponents and plotting the
Poincar\'{e} sections as these two parameters are varied and, in particular,
find that the largest Lyapunov exponents evaluated within a range of values of
$\kappa$ are above that is computed at $\kappa=0$, for $\kappa p_\phi < 0$. We
also give estimates of the critical exponents for the Lyapunov exponent as the
system transits from the chatoic to non-chaotic phase with $p_\phi$ approaching
to a critical value.
