  This paper examines the Stark effect, as a first order perturbation of
manifestly covariant hydrogen-like bound states. These bound states are
solutions to a relativistic Schr\"odinger equation with invariant evolution
parameter, and represent mass eigenstates whose eigenvalues correspond to the
well-known energy spectrum of the non-relativistic theory. In analogy to the
nonrelativistic case, the off-diagonal perturbation leads to a lifting of the
degeneracy in the mass spectrum. In the covariant case, not only do the
spectral lines split, but they acquire an imaginary part which is lnear in the
applied electric field, thus revealing induced bound state decay in first order
perturbation theory. This imaginary part results from the coupling of the
external field to the non-compact boost generator. In order to recover the
conventional first order Stark splitting, we must include a scalar potential
term. This term may be understood as a fifth gauge potential, which compensates
for dependence of gauge transformations on the invariant evolution parameter.
