First-order equivalent to Einstein-Hilbert Lagrangian

A first-order Lagrangian $L^\nabla $ variationally equivalent to the second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by $L^\nabla $ is proved to be regular and its Hamiltonian formulation is studied, including its covariant Hamiltonian attached to $\nabla $.