This paper presents the chaotic analysis of the single-walled carbon nanotubes on elastic medium. Due to small scales of the nanotubes, the nonlocal elastic theory is applied. Besides, due to large-amplitude vibrations of the nanotubes, the geometrical nonlinearity is taken into account, so the von Kármán strain is incorporated. The results show that the period-three oscillation, the chaos and the period-one oscillation are excited by the different excitation amplitudes. In addition, the excitation amplitude of the chaos increases as the nonlocal parameter increases. These results are also validated by the steady-state time responses, the FFT spectrums, the phase portraits, and the Poincaré sections.