No Vacuum Cerenkov Radiation Losses in the Timelike Lorentz-Violating Chern-Simons Theory

In a Lorentz- and CPT-violating modification of electrodynamics that includes a timelike Chern-Simons term, there are no energy losss through vacuum Cerenkov radiation. A charge moving with a constant velocity does not lose energy, because of an unusual cancellation. Higher frequency modes of the electromagnetic field carry away positive energy, but lower frequency modes carry away a compensating negative amount of energy.