  Using a covariant formalism, we construct a chiral kinetic theory Lorentz
invariant to order $\mathcal O(\hbar)$ which includes collisions. We find a new
contribution to the particle number current due to the side jumps required by
the conservation of angular momentum during collisions. We also find a
conserved symmetric stress-energy tensor as well as the $H$-function obeying
Boltzmann's $H$-theorem. We demonstrate their use by finding a general
equilibrium solution and the values of the anomalous transport coefficients
characterizing chiral vortical effect.
