  We point out that unitary representations of the Virasoro algebra contain
Berry phases obtained by acting on a primary state with conformal
transformations that trace a closed path on a Virasoro coadjoint orbit. These
phases can be computed exactly thanks to the Maurer-Cartan form on the Virasoro
group, and they persist after combining left- and right-moving sectors.
Thinking of Virasoro representations as particles in AdS_3 dressed with
boundary gravitons, the Berry phases associated with Brown-Henneaux
diffeomorphisms provide a gravitational extension of Thomas precession.
