An experiment is in progress at the Los Alamos Meson Physics Facility (LAMPF) to determine with high precision the hyperfine structure interval /spl Delta/v (to /spl sim/10 ppb) and the muon to proton magnetic moment ratio /spl mu//sub /spl mu////spl mu//sub p/(to /spl sim/60 ppb) in the ground state of muonium (/spl mu//sup +/e/sup -/). These precision goals correspond to increases in precision of /spl Delta/v and of /spl mu//sub /spl mu////spl mu//sub p/ by about a factor of 5 compared to present knowledge.