  We present a determination of the molecular gas mass in the AU Microscopii
circumstellar disk. Direct detection of a gas component to the AU Mic disk has
proven elusive, with upper limits derived from ultraviolet absorption line and
submillimeter CO emission studies. Fluorescent emission lines of H2, pumped by
the OVI 1032 resonance line through the C-X (1 -- 1) Q(3) 1031.87 \AA\
transition, are detected by the Far Ultraviolet Spectroscopic Explorer. These
lines are used to derive the H2 column density associated with the AU Mic
system. The derived column density is in the range N(H2) = 1.9 x 10^{17} - 2.8
x 10^{15} cm^{-2}, roughly two orders of magnitude lower than the upper limit
inferred from absorption line studies. This range of column densities reflects
the range of H2 excitation temperature consistent with the observations, T(H2)
= 800 -- 2000 K, derived from the presence of emission lines excited by OVI in
the absence of those excited by LyA. Within the observational uncertainties,
the data are consistent with the H2 gas residing in the disk. The inferred
N(H2) range corresponds to H2-to-dust ratios of < 1/30:1 and a total M(H2) =
4.0 x 10^{-4} - 5.8 x 10^{-6} Earth masses. We use these results to predict the
intensity of the associated rovibrational emission lines of H2 at infrared
wavelengths covered by ground-based instruments, HST-NICMOS, and the
Spitzer-IRS.
