  We consider a class of time dependent finite energy multi-soliton solutions
of the U(N) integrable chiral model in $(2+1)$ dimensions. The corresponding
extended solutions of the associated linear problem have a pole with arbitrary
multiplicity in the complex plane of the spectral parameter. Restrictions of
these extended solutions to any spacelike plane in $\R^{2,1}$ have trivial
monodromy and give rise to maps from a three sphere to U(N). We demonstrate
that the total energy of each multi-soliton is quantised at the classical level
and given by the third homotopy class of the extended solution. This is the
first example of a topological mechanism explaining classical energy
quantisation of moving solitons.
