High harmonic generation (HHG) by atoms subjected to an intense laser field is a major topic in nonlinear atomic physics. Classically, a particle under an intense driving force can exhibit chaos. I present results of numerical simulations for classical phase space structure and classical and quantum spectra of the particle motion. I also compare the spectrum of regular motion and that of chaotic motion under the same conditions. The results indicate that there can be some connections between high harmonic generation and chaotic motion.