The classical dynamics of highly chaotic vibrational dynamics is studied via the nature of resonance zones. It is demonstrated that the flow into and out of the resonance zones is complicated with some trajectories spending less than one period outside before reentering, referred to here as "virtual recrossing." Despite the strong chaos, an approximate semiclassical quantization method based on the resonance zone structure can be used to generate eigenvalues to within a few percent of the quantum values well into the chaotic regime. The semiclassical quantization allows for the assignment of highly excited, strongly mixed vibrational eigenstates.