We search for rare charm decays of the form X_c^+\to h^\pm \ell^+\ell^\mp, where X_c^+ is a charm hadron, h^\pm can be a pion, kaon or proton and \ell^\pm is an electron or a muon. In the pion and kaon modes we search for both D+ and Ds+ decays, while in the proton modes we search for Lambda_c+ decays. The search is performed using data collected by the BaBar experiment near \sqrt{s} = 10.6 GeV.