A dynamical model for the piezoelectric plate vibrations is presented in this letter. The calculations of phase portrait and Lyapunov exponents based on the coupled-mode equations given by the theoretical model show that the vibrations of a piezoelectric plate resonator under the resonance may exhibit the chaotic behavior. The experiment is carried out for a LiNbO3 thickness-longitudinal vibration plate resonator by using a setup based on heterodyne laser probe. The fractional harmonic vibration as well as chaotic behaviors are observed.