  We report on the first complete calculation of the $K_L-K_S$ mass difference,
$\Delta M_K$, using lattice QCD. The calculation is performed on a 2+1 flavor,
domain wall fermion ensemble with a 330MeV pion mass and a 575 MeV kaon mass.
We use a quenched charm quark with a 949 MeV mass to implement
Glashow-Iliopoulos-Maiani cancellation. For these heavier-than-physical
particle masses, we obtain $\Delta M_K =3.19(41)(96)\times 10^{-12}$ MeV, quite
similar to the experimental value. Here the first error is statistical and the
second is an estimate of the systematic discretization error. An interesting
aspect of this calculation is the importance of the disconnected diagrams, a
dramatic failure of the OZI rule.
