An anomalous light shift in the precession of a ground-state Zeeman coherence is observed: The Larmor frequency increases with the strength of a drive that is blue (red) detuned from a transition out of the lower (upper) energy level. Our measurements are made on Rb-85 atoms traversing an optical cavity containing a few photons; shifts as large as 1% per photon are recorded. The anomalous shift arises from an accumulation of phase driven by quantum jumps. It is stochastic and accompanied by broadening.