  We study the most general renormalizable ${\cal N}=1$ $U(N)$ Chern-Simons
gauge theory coupled to a single (generically massive) fundamental matter
multiplet. At leading order in the 't Hooft large $N$ limit we present
computations and conjectures for the $2 \times 2$ $S$ matrix in these theories;
our results apply at all orders in the 't Hooft coupling and the matter self
interaction. Our $S$ matrices are in perfect agreement with the recently
conjectured strong weak coupling self duality of this class of theories. The
consistency of our results with unitarity requires a modification of the usual
rules of crossing symmetry in precisely the manner anticipated in
arXiv:1404.6373, lending substantial support to the conjectures of that paper.
In a certain range of coupling constants our $S$ matrices have a pole whose
mass vanishes on a self dual codimension one surface in the space of couplings.
