It is shown that a time-evolving strange attractor formed by a dynamical contact of two logistic maps, a special case of the so-called interior crisis, can generate rhythmic hopping with a chaotic fluctuation between two domains on which the individual logistic maps are defined. A variety of distributions of the hopping time have been obtained with different choices of an evolution parameter in the map. The physical mechanism and the conditions for the rhythmic hopping are discussed. \textcopyright{} 1996 The American Physical Society.