  We present a first-principles CFT calculation corresponding to the spherical
collapse of a shell of matter in three dimensional quantum gravity. In field
theory terms, we describe the equilibration process, from early times to
thermalization, of a CFT following a sudden injection of energy at time t=0. By
formulating a continuum version of Zamolodchikov's monodromy method to
calculate conformal blocks at large central charge c, we give a framework to
compute a general class of probe observables in the collapse state,
incorporating the full backreaction of matter fields on the dual geometry. This
is illustrated by calculating a scalar field two-point function at time-like
separation and the time-dependent entanglement entropy of an interval, both
showing thermalization at late times. The results are in perfect agreement with
previous gravity calculations in the AdS$_3$-Vaidya geometry. Information loss
appears in the CFT as an explicit violation of unitarity in the 1/c expansion,
restored by nonperturbative corrections.
