The energy spectrum of the highly excited states of a quantum Daffing oscillator is considered. It is shown that the energy levels satisfy En>En+1 and En → -F2/8ω2, when n → ∞, where F2 and ω are the intensity and frequency of the external field. It is suggested that this property of the spectrum is the quantum manifestation of a stochastic attractor in the classical nonlinear limit. This property also takes place for large F2.