  We establish interior Lipschitz regularity for continuous viscosity solutions
of fully nonlinear, conformally invariant, degenerate elliptic equations. As a
by-product of our method, we also prove a weak form of the strong comparison
principle, which we refer to as the principle of propagation of touching
points, for operators of the form $\nabla^2 \psi + L(x,\psi,\nabla \psi)$ which
are non-decreasing in $\psi$.
