  We consider a fifth force to be an interaction that couples to matter with a
strength that grows with the number of atoms. In addition to competing with the
strength of gravity a fifth force can give rise to violations of the
equivalence principle. Current long range constraints on the strength and range
of fifth forces are very impressive. Amongst possible fifth forces are those
that couple to lepton flavorful charges $L_e-L_{\mu}$ or $L_e-L_{\tau}$. They
have the property that their range and strength are also constrained by
neutrino interactions with matter. In this brief note we review the existing
constraints on the allowed parameter space in gauged $U(1)_{L_e-L_{\mu},
L_{\tau}}$. We find two regions where neutrino oscillation experiments are at
the frontier of probing such a new force. In particular, there is an allowed
range of parameter space where neutrino matter interactions relevant for long
baseline oscillation experiments depend on the depth of the neutrino beam below
the surface of the earth.
