  We carry out the non-perturbative renormalization of the chromo-magnetic
operator in Heavy Quark Effective Theory. At order 1/m of the expansion, the
operator is responsible for the mass splitting between the pseudoscalar and
vector B mesons. We obtain its two-loop anomalous dimension in a Schr"odinger
functional scheme by successive one-loop conversions to the lattice MS scheme
and the MS-bar scheme. We then compute the scale evolution of the operator
non-perturbatively in the N_f=0 theory between $\mu \approx 0.3$ GeV and $\mu
\approx 100$ GeV, where contact is made with perturbation theory. The overall
renormalization factor that converts the bare lattice operator to its
renormalization group invariant form is given for the Wilson gauge action and
two standard discretizations of the heavy-quark action. As an application, we
find that this factor brings the previous quenched predictions of the B* - B
mass splitting closer to the experimental value than found with a perturbative
renormalization. The same renormalization factor is applicable to the
spin-dependent potentials of Eichten and Feinberg.
