  An action for simplicial euclidean general relativity involving only
left-handed fields is presented. The simplicial theory is shown to converge to
continuum general relativity in the Plebanski formulation as the simplicial
complex is refined. This contrasts with the Regge model for which Miller and
Brewin have shown that the full field equations are much more restrictive than
Einstein's in the continuum limit. The action and field equations of the
proposed model are also significantly simpler then those of the Regge model
when written directly in terms of their fundamental variables.
  An entirely analogous hypercubic lattice theory, which approximates
Plebanski's form of general relativity is also presented.
