The branching fraction for a previously unobserved decay D*+ [RIGHTWARDS ARROW] D+ e+ e[-] is pres s dicted theoretically in this dissertation to be 0.65% of the branching fraction for the decay D*+ [RIGHTWARDS ARROW] D+ [gamma]. We conduct a search for the D*+ [RIGHTWARDS ARROW] D+ e+ e[-] in 586 pb[-]1 s s s s of e+ e[-] collision data collected with the CLEO-c detector at the Cornell Electron Storage Ring (CESR) operating at a center of mass energy of 4170 MeV and observe it with a significance of 6.4 [sigma] over estimated backgrounds. The ratio of branching fractions B(D*+ [RIGHTWARDS ARROW] D+ e+ e[-] )/ B(D*+ [RIGHTWARDS ARROW] D+ [gamma]) is measured to be s s s s (0.72 ± 0.14(stat) ± 0.06(syst))%, which is within one standard deviation of uncertainty from the predicted value.