  Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a
mathematically precise quantization of the Hamiltonian Chern-Simons theory. We
introduce the Chern-Simons theory on the lattice which is expected to reproduce
the results of the continuous theory exactly. The lattice model enjoys the
symmetry with respect to a quantum gauge group. Using this fact we construct
the algebra of observables of the Hamiltonian Chern-Simons theory equipped with
a *-operation and a positive inner product.
