  The local Gauss law of quantum chromodynamics on a finite lattice is
investigated. It is shown that it implies a gauge invariant, additive law
giving rise to a gauge invariant ${\mathbb Z}_3$-valued global charge in QCD.
The total charge contained in a region of the lattice is equal to the flux
through its boundary of a certain ${\mathbb Z}_3$-valued, additive quantity.
Implications for continuous QCD are discussed.
