  We construct a 1d spin chain Hamiltonian with generic interactions and prove
that the thermal correlation functions of the model admit an explicit random
matrix representation. As an application of the result, we show how the
observables of $U(N)$ Chern-Simons theory on $S^{3}$ can be reproduced with the
thermal correlation functions of the 1d spin chain, which is of the XX type,
with a suitable choice of exponentially decaying interactions between
infinitely many neighbours. We show that for this model, the correlation
functions of the spin chain at a finite temperature $\beta =1$ give the
Chern-Simons partition function, quantum dimensions and the full topological
$S$-matrix.
