We report the first observation of diffractively produced open charm in 800-GeV/c pp collisions of the type pp-->pD*X. We measure cross sections of sigma(diff)(D*+) = (0.185+/-0.044+/-0.054) (mu)b and sigma(diff)(D(*-)) = (0.174+/-0.034+/-0.029) (mu)b. Our measurements are based on 4.3x10(9) events recorded by FNAL E690 in the fixed-target run of 1991. We compare our results with previous fixed-target charm experiments.