We report the observation of resonant Raman scattering in the strong coupli
ng regime for a planar microcavity containing cyanine dye J aggregates. The
giant Rabi splitting between the polariton branches, resulting from the ve
ry large exciton oscillator strengths, allows the observation of doubly res
onant Raman scattering where both incident and scattered photons are in res
onance with the mixed exciton-cavity-mode states. Under double resonance co
nditions the Raman signals are found to be very significantly enhanced, by
factors up to 300, relative to noncavity organic films.