  A geometric multisymplectic formulation of the classical BRST symmetry of
constrained first-order classical field theories is described. To effect this
we introduce graded analogues of the bundles and manifolds of the
multisymplectic formulation of first-order field theories.
  The Lagrange-d'Alembert formalism is also developed in terms of the
multisymplectic framework. The result is a covariant Hamiltonian BFV formalism.
