This paper studies the spectral properties of the Laplace-Beltrami Laplacian
with an $L^\infty$ drift term. We obtain a lower bound for the principle
eigenvalue for the Dirichlet problem and a lower bound for any real eigenvalues
of the operator of compact manifold. We make no assumptions of self-adjointness
or that the drift has any additional regularity. In the self-adjoint case of a
Witten Laplacian, our work improves the current theory by proving an estimate
that does not rely on a bound on the Bakry-Emery Ricci tensor.