  We discuss the phenomenology of a light U(1) gauge boson, $\gamma_B$, that
couples only to baryon number. We assume that the new U(1) gauge symmetry is
spontaneously broken and that the $\gamma_B$ mass is smaller than $m_Z$.
Nevertheless, we show that the model survives the current experimental
constraints. In addition, we argue that evidence for the existence of such a
particle could be hidden in existing LEP and Tevatron data. We determine the
allowed regions of the $m_B$-$\alpha_B$ plane, where $m_B$ is the $\gamma_B$
mass, and where $4 \pi \alpha_B$ is the squared gauge coupling. We point out
that in some parts of the allowed parameter space our model can account for
rapidity gap events in proton-antiproton scattering seen at the Fermilab
Tevatron.
