  We investigate whether rings around extrasolar planets could be detected from
those planets' transit lightcurves. To this end we develop a basic theoretical
framework for calculating and interpreting the lightcurves of ringed planet
transits based on the existing framework used for stellar occultations, a
technique which has been effective for discovering and probing ring systems in
the solar system. We find that the detectability of large, Saturn-like ring
systems is largest during ingress and egress, and that reasonable photometric
precisions of $\sim 1-3 \times 10^{-4}$ with 15-minute time resolution should
be sufficient to discover such ring systems. For some ring particle sizes,
diffraction around individual particles leads to a detectable level of
forward-scattering that can be used to measure modal ring particle diameters.
An initial census of large ring systems can be carried out using high-precision
follow-up observations of detected transits and by the upcoming NASA
\emph{Kepler} mission. The distribution of ring systems as a function of
stellar age and as a function of planetary semimajor axis will provide
empirical evidence to help constrain how rings form and how long rings last.
