We discover hidden Rashba fine structure in CH3NH3PbI3 and demonstrate its quantum control by vibrational coherence through symmetry-selective vibronic (electron-phonon) coupling. Above a critical threshold of a single-cycle terahertz pump field, a Raman phonon mode distinctly modulates the middle excitonic states with persistent coherence for more than ten times longer than the ones on two sides that predominately couple to infrared phonons. These vibronic quantum beats, together with first-principles modeling of phonon periodically modulated Rashba parameters, identify a threefold excitonic fine structure splitting, i.e., optically forbidden, degenerate dark states in between two bright ones with a narrow, similar to 3 nm splitting. Harnessing of vibronic quantum coherence and symmetry inspires light-perovskite quantum control and sub-THz-cycle Rashba engineering of spin-split bands for ultimate multifunction device
