  We search for rare FCNC charm decays of the form $X_c^+\to h^+\llp$, where
$X_c^+$ is a charm hadron, $h$ is a pion, kaon or proton, and $\ell^{(}{'}^{)}$
is an electron or a muon. In the pion and kaon modes, we study both $D^+$ and
$D_s^+$ decays, while in the proton modes we study $\Lambda_c^+$ decays. Based
on a data sample of 288${fb}^{-1}$ of $e^+e^-$ collisions collected by BABAR,
we set preliminary 90% confidence level limits between 4 to 40$\times10^{-6}$
for the branching fractions of the different decay modes. For most decay modes,
our analysis provides a significant improvement over previous results.
