The regime of passive mode locking in a Ti:sapphire laser with a coherent absorber resulting in the emission of pulses with a duration considerably shorter than the absorber relaxation times is demonstrated experimentally. A cell filled with rubidium vapor placed in the laser cavity serves as a coherent absorber. Mode locking arises when the laser oscillation frequency is tuned to the resonance transitions in rubidium. In our opinion, 2π pulses of self-induced transparency appear in the cavity, and the reported results represent the first experimental demonstration of passive mode locking caused by the effect of self-induced transparency, which has previously been discussed only theoretically.