We report a new kind of "dynamical tunneling" that can be observed in chaotic molecular vibration. The present phenomenon has been found in eigenfunctions quantized in a thin quasiseparatrix (chaotic zone) in phase space. On the classical Poincare section corresponding to this situation, two or more unstable (hyperbolic) fixed points coexist and are connected through the so-called heteroclinic crossings, whereby the entire quasiseparatrix is generated. When the quasiseparatrix is thin enough, each of the hyperbolic fixed points is surrounded by the relatively "wide lake" of chaos due to the infinite and violent crossings between the stable and unstable manifolds, and these lakes are in turn connected by "narrow canals." Our finding is, in spite of the fact that the narrow canals are classically allowed for the trajectories to pass through fast, wave packets can be quantized predominantly as "quasistanding-waves" in each lake area and hence can be mostly localized to remain there for much longer time than the corresponding classical trajectories do. In other words, the wave packets are localized in the vicinity of the classically unstable fixed points due to the quantum effect. However, a pair of these "localized" wave packets are eventually delocalized into the other lakes, and thereby form a pair of eigenfunctions (purely standing waves) with a small level splitting. Thus the present phenomenon can be characterized as a tunneling between the states of quantum localization in an oscillator problem.