  In this paper we prove a sequential convergence result for blowup solutions
to the $m$-equivariant, self-dual Chern--Simons--Schr{\"o}dinger equation. We
show that if $u$ has mass less than twice the mass of the soliton, a blowup
solution converges to the soliton along a subsequence of times that converges
to the blowup time.
