  In this paper we consider a two-phase free boundary problem ruled by the
infinity Laplacian. Our main result states that bounded viscosity solutions in
$B_1$ are universally Lipschitz continuous in $B_{1/2}$, which is the optimal
regularity for the problem. We make a new use of the Ishii-Lions' method, which
works as a surrogate for the lack of a monotonicity formula and is bound to be
applicable in related problems.
