We have searched for spontaneous conversion of muonium (M) to antimuonium M bar by a method involving detection of high-Z muonic X rays. A beam of M atoms with keV energies, produced by electron pickup by ..mu../sup +/ from a foil, travels in vacuum and in a magnetic field-free environment to a high-Z target. The event signatures used were a double coincidence of two muonic X rays of the target material and a triple coincidence that also required detection of secondary electrons ejected when M strikes the target. Partial analysis of our 8 x 10/sup 6/ triggers indicates upper limits on the effective M ..-->..M bar four-dermion coupling constant of G/sub MM bar/ less than or equal to 30 G/sub F/ (90% C.L.) and G/sub MM bar/ less than or equal to 8 G/sub F/ (90% C.L.), respectively, from the two signatures. This begins to probe predictions of the left-right symmetric theory with a doubly-charged Higgs triplet
