  We explore the effective field theory of a vector field $X^\mu$ that has a
St\"uckelberg mass. The absence of a gauge symmetry for $X^\mu$ implies
Lorentz-invariant operators are constructed directly from $X^\mu$. Beyond the
kinetic and mass terms, allowed interactions at the renormalizable level
include $X_\mu X^\mu H^\dagger H$, $(X_\mu X^\mu)^2$, and $X_\mu j^\mu$, where
$j^\mu$ is a global current of the SM or of a hidden sector. We show that all
of these interactions lead to scattering amplitudes that grow with powers of
$\sqrt{s}/m_X$, except for the case of $X_\mu j^\mu$ where $j^\mu$ is a
nonanomalous global current. The latter is well-known when $X$ is identified as
a dark photon coupled to the electromagnetic current, often written
equivalently as kinetic mixing between $X$ and the photon. The power counting
for the energy growth of the scattering amplitudes is facilitated by isolating
the longitudinal enhancement. We examine in detail the interaction with an
anomalous global vector current $X_\mu j_{anom}^\mu$, carefully isolating the
finite contribution to the fermion triangle diagram. We calculate the
longitudinally-enhanced observables $Z \rightarrow X\gamma$ (when $m_X < m_Z$),
$f\bar{f} \rightarrow X \gamma$, and $Z\gamma \to Z\gamma$ when $X$ couples to
the baryon number current. Introducing a fake gauge-invariance by writing
$X^\mu = A^\mu - \partial^\mu \pi/m_X$, the would-be gauge anomaly associated
with $A_\mu j_{anom}^\mu$ is canceled by $j_{anom}^\mu \partial_\mu \pi/m_X$;
this is the four-dimensional Green-Schwarz anomaly-cancellation mechanism at
work. Our analysis suggests there is no free lunch by appealing to
St\"uckelberg for the mass of a vector field: the price paid for avoiding a
dark Higgs sector is replaced by the non-generic set of interactions that the
St\"uckelberg vector field must have to avoid amplitudes that grow with energy.
