The classical pyrochlore antiferromagnet (AFM) is considered the ``most'' geometrically frustrated system.  Classically, this leads to the absence of any ordering transition at non-zero temperature, even in an applied magnetic field.  Recent experiments on the spinel chromites, ACr₂O₄ (A=Cd,Hg) show a very robust magnetization plateau in a strong magnetic field with a simultaneous magnetic ordering.  We describe a model of spin-lattice coupling that explains both the plateau formation and the observed ordering on the plateau. The predictions are confirmed by recent neutron scattering and x-ray scattering experiments (S. H. Lee et al.).  The same model applied to zero magnetic field predicts a reduced but still large ground state degeneracy, including the states observed in both the Cd and Hg materials.  This is consistent with the dominance of spin-lattice interactions, with weak additional effects determining the low field magnetic ordering.