  The gravitational acceleration of antimatter, $\bar{g}$, has never been
directly measured and could bear importantly on our understanding of gravity,
the possible existence of a fifth force, and the nature and early history of
the universe. Only two avenues for such a measurement appear to be feasible:
antihydrogen and muonium. The muonium measurement requires a novel,
monoenergetic, low-velocity, horizontal muonium beam directed at an atom
interferometer. The precision three-grating interferometer can be produced in
silicon nitride or ultrananocrystalline diamond using state-of-the-art
nanofabrication. The required precision alignment and calibration at the
picometer level also appear to be feasible. With 100 nm grating pitch, a 10%
measurement of $\bar{g}$ can be made using some months of surface-muon beam
time, and a 1% or better measurement with a correspondingly larger exposure.
This could constitute the first gravitational measurement of leptonic matter,
of 2nd-generation matter and, possibly, the first measurement of the
gravitational acceleration of antimatter.
