Transparency and perfect absorption are two contradictory terms; a perfect absorber never permits waves to transmit through. However, this statement only remains true in the linear regime, where the nonlinearity has been omitted and the physical system like the perfect absorber is not affected by the incoming waves. Here we experimentally demonstrate an intriguing self-induced transparency effect in a perfectly absorbing optical microcavity, which perfectly absorbs any incoming waves at the low power level, but allows a portion of waves to be transmitted at the higher power due to the nonlinear coupling between the fundamental and its second harmonic modes. Moreover, the asymmetric scattering nature of the microcavity enables a chiral and unidirectional reflection in one of the input ports, this leads to asymmetric and chiral coherent control of the perfect absorption states through phase varying. More importantly, such chiral behaviors also empower the chiral emission of second-harmonic generation with a high distinct ratio in the transparency state. These results pave the way for controllable transparency in a wide range of fields in optics, microwaves, acoustics, mechanics, and matter waves.