A new form of induced transparency enabled by dynamical tunneling coupling of continuous chaos and discrete regular modes in a slightly deformed optical microcavity is demonstrated experimentally. An optical beam is focused on the cavity boundary and tuned on resonance with a high-Q mode, which leads to destructive interference for the excitation of chaotic field and induces a transparency in the transmission. The experimental results are in excellent agreement with a model based on quantum scattering theory. This tunneling-induced transparency is accompanied by extremely steep normal dispersion, and holds great potential in slow light and enhanced nonlinear interactions. [ABSTRACT FROM AUTHOR]