  The FASER experiment at the LHC is designed to search for light,
weakly-interacting particles produced in proton-proton collisions at the ATLAS
interaction point that travel in the far-forward direction. The first results
from a search for dark photons decaying to an electron-positron pair, using a
dataset corresponding to an integrated luminosity of 27.0 fb$^{-1}$ collected
at center-of-mass energy $\sqrt{s} = 13.6$ TeV in 2022 in LHC Run 3, are
presented. No events are seen in an almost background-free analysis, yielding
world-leading constraints on dark photons with couplings $\epsilon \sim 2
\times 10^{-5} - 1 \times 10^{-4}$ and masses $\sim$ 17 MeV - 70 MeV. The
analysis is also used to probe the parameter space of a massive gauge boson
from a U(1)$_{B-L}$ model, with couplings $g_{B-L} \sim 5 \times 10^{-6} - 2
\times 10^{-5}$ and masses $\sim$ 15 MeV - 40 MeV excluded for the first time.
