  This paper is devoted to proving that, in QCD, the lightest glueball state
must be the scalar with $J^{PC} = 0^{++}$. The proof relies upon the positivity
of the path integral measure in Euclidean space and the fact that interpolating
fields for all spins can be bounded by powers of the scalar glueball operator.
The problem presented by the presence of vacuum condensates is circumvented by
considering the time evolution of the propagators and exploiting the positivity
of the Hamiltonian.
