  The quantisation of the reduced first-order dynamics of the nonrelativistic
model for Chern-Simons vortices introduced by Manton is studied on a sphere of
given radius. We perform geometric quantisation on the moduli space of static
solutions, using a Kaehler polarisation, to construct the quantum Hilbert
space. Its dimension is related to the volume of the moduli space in the usual
classical limit. The angular momenta associated with the rotational SO(3)
symmetry of the model are determined for both the classical and the quantum
systems. The results obtained are consistent with the interpretation of the
solitons in the model as interacting bosonic particles.
