The chiral kinetic theory is a pivotal theoretical tool for the transport theory of massless degrees of freedom. Despite various developments, the usual framework contains only linear-order quantum corrections. In this talk, I will explain the formulation of the chiral kinetic theory with the nonlinear-order corrections. Also I will show several findings from this nonlinear chiral kinetic theory, such as nondissipative transport phenomena, a consistency with the Euler-Heisenberg effective theory and a potential issue on regularization.