  The action of the free $\mathcal{N} = (3,1)$ theory in six spacetime
dimensions is explicitly constructed. The variables of the variational
principle are prepotentials adapted to the self-duality conditions on the
fields. The $(3,1)$ supersymmetry variations are given and the invariance of
the action is verified. The action is first-order in time derivatives. It is
also Poincar\'e invariant but not manifestly so, just like the Hamiltonian
action of more familiar relativistic field theories.
