We propose a new a posteriori error estimate for Hamilton- Jacobi equations which is independent of the Hamiltonian, the space dimension, and of the way the approximate solution is computed; moreover, it is local. This unique a posteriori error estimate allows us to construct a simple, recursive adaptive algorithm with which we can achieve a rigorous error control even in the presence of discontinuities in the derivatives. The algorithm can be applied to any explicit and stable numerical scheme; moreover, the algorithm uses a local space-time refinement strategy that does not alter the stability condition of the numerical scheme. This is joint work with Jianliang Qian, IMA, University of Minnesota.