  We study the nine possible rare charm meson decays D->Pl^+l^-
(P=pi,K,eta,eta') using the Heavy Meson Chiral Lagrangians and find them to be
dominated by the long distance contributions. The decay D^+ -> pi^+l^+l^- with
the branching ratio 1*10^(-6) is expected to have the best chances for an early
experimental discovery. The short distance contribution in the five Cabibbo
suppressed channels arises via the c->ul^+l^- transition; we find that this
contribution is detectable only in the D->pi l^+l^- decay, where it dominates
the differential spectrum at high-q^2. The general Minimal Supersymmetric
Standard Model can enhance the c->ul^+l^- rate by up to an order of magnitude;
its effect on the D->Pl^+l^- rates is small since the c->ul^+l^- enhancement is
sizable in low-q^2 region, which is inhibited in the hadronic decay.
