  We have searched for a light vector boson $U$, the possible carrier of a
"dark force", with the KLOE detector at the DA$\Phi$NE \epm\ collider,
motivated by astrophysical evidence for the presence of dark matter in the
universe. Using \epm\ collisions collected with an integrated luminosity of
$239.3$~pb$^{-1}$, we look for a dimuon mass peak in the reaction \epm\to$\mu^+
\mu^-$\gam, corresponding to the decay $U\to\mu^+\mu^-$. We find no evidence
for a $U$ vector boson signal. We set a 90\% CL upper limit for the mixing
parameter squared between the photon and the $U$ boson of 1.6$\times$10$^{-5}$
to 8.6$\times$10$^{-7}$ for the mass region $520<m_{\rm U}<980$ MeV.
