The influence of chaos on tunneling in the quantum phase space of the harmonically driven pendulum is studied herein. We analyze the avoided level crossing between a quasienergy state associated with the chaotic part of the phase space and a member of the nearly degenerate doublet localized on the symmetric Kolmogorov-Arnold-Moser (KAM) islands. As a result of the interaction the quasienergy states ``exchange'' their structure. The initially chaotic state evolves into the regular one and vice versa. This interchange significantly affects dynamical tunneling of wave packets centered on the KAM islands.