We consider a measurement of the gravitational acceleration of antimatter, gbar, using muonium. A monoenergetic, low-velocity, horizontal muonium beam will be formed from a surface-muon beam using a novel technique and directed at an atom interferometer. The measurement requires a precision three-grating interferometer: the first grating pair creates an interference pattern which is analyzed by scanning the third grating vertically using piezo actuators. State-of-the-art nanofabrication can produce the needed membrane grating structure in silicon nitride or ultrananoscrystalline diamond. With 100 nm grating pitch, a 10% measurement of gbar can be made using some months of surface-muon beam time. This will be the first gravitational measurement of leptonic matter, of 2nd-generation matter and, possibly, the first measurement of the gravitational acceleration of antimatter.
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