  In this article we establish the unconditional uniqueness of solutions to an
Infinite Radial Chern-Simons-Schr\"odinger (IRCSS) hierarchy in two spatial
dimensions. The IRCSS hierarchy is a system of infinitely many coupled PDEs
that describes the limiting Chern-Simons-Schr\"odinger dynamics of infinitely
many interacting anyons. The anyons are two dimensional objects which interact
through a self-generated field. Due to the interactions with the self-generated
field, the IRCSS hierarchy is a system of nonlinear PDEs, which distinguishes
it from the linear infinite hierarchies studied previously. Factorized
solutions of the IRCSS hierarchy are determined by solutions of the
Chern-Simons-Schr\"odinger system. Our result therefore implies the
unconditional uniqueness of solutions to the radial Chern-Simons-Schr\"odinger
system as well.
