  We study chaotic inflation with a Galileon-like self interaction
$G(\phi,X)\Box \phi$, where $G(\phi,X)\propto X^{n}$. 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 $n_{\mathcal{S}}-r$ 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.
