We study chaotic inflation with a Galileon-like self-interaction G(ϕ, X) □ ϕ, where G(ϕ, X) ∝ Xn. General conditions required for successful inflation are deduced and discussed from the background and cosmological perturbations under slow-roll approximation. Interestingly, it is found that in the regime where the Galileon term dominates over the standard kinetic term, the tensor-to-scalar ratio becomes significantly suppressed in comparison to the standard expression in General Relativity (GR). Particularly, we find the allowed range in the space of parameters characterizing the chaotic quadratic and quartic inflation models by considering the current observational data of Planck from the nS- r plane. Finally, we discuss about the issue if the Galileon term is dominant by the end of inflation, this can affect the field oscillation during reheating.