  For a simply connected, compact, simple Lie group G, the moduli space of flat
G-bundles over a closed surface is known to be pre-quantizable at integer
levels. For non-simply connected G, however, integrality of the level is not
sufficient for pre-quantization, and this paper determines the obstruction --
namely a certain cohomology class in H^3(G^2;Z) -- that places further
restrictions on the underlying level. The levels that admit a pre-quantization
of the moduli space are determined explicitly for all non-simply connected,
compact, simple Lie groups G.
