  In this work, we formulate the theory of Lorentz-violating scalar Quantum
Chromodynamics with an arbitrary non-Abelian gauge group. This theory belongs
to the class of models encompassed by the standard model extension framework.
At the lowest order in the theory's Lorentz violation parameters, we calculate
the divergent quantum corrections, including the renormalization group
$\beta$-functions of the theory. The Lorentz-violating sector is shown to be
scale invariant if there is a particular relation between the couplings.
