  We present a high order scheme for approximating kinetic equations with stiff
relaxation. The objective is to provide efficient methods for solving the
underlying system of conservation laws. The construction is based on several
ingredients: (i) a high order implicit upwind Discontinuous Galerkin
approximation of the kinetic equations with easy-to-solve triangular linear
systems; (ii) a second order asymptotic-preserving time integration based on
symmetry arguments; (iii) a palindromic composition of the second order method
for achieving higher orders in time. The method is then tested at orders 2, 4
and 6. It is asymptotic-preserving with respect to the stiff relaxation and
accepts high CFL numbers.
