  We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS) under
equivariant symmetry, which is a $L^{2}$-critical equation. It is known that
(CSS) admits solitons and finite-time blow-up solutions. In this paper, we show
soliton resolution for any solutions with equivariant data in the weighted
Sobolev space $H^{1,1}$: every maximal solution decomposes into at most one
modulated soliton and a radiation. A striking fact is that the nonscattering
part must be a single modulated soliton. To our knowledge, this is the first
result on soliton resolution in a class of nonlinear Schr\"odinger equations
which are not known to be completely integrable. The key ingredient is the
defocusing nature of the equation in the exterior of a soliton profile. This is
a consequence of two distinctive features of (CSS): self-duality and non-local
nonlinearity.
