When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a $B\wedge F$ coupling and a kinetic term for $B$ is included, the gauge field develops an effective mass. The theory can be made invariant under a non-abelian vector gauge symmetry by introducing an auxiliary vector field. The covariant quantization of this theory requires ghosts for ghosts. The resultant theory including gauge fixing and ghost terms is BRST-invariant by construction, and therefore unitary. The construction of the BRST-invariant action is given for both abelian and non-abelian models of mass generation.

15 pages, revtex