  SDSS J083942.11+380526.3 is an Iron Low-ionization Broad Absorption Line
(FeLoBAL) quasar at z = 2.3, and Aoki et al. (2006) recently found the presence
of an H alpha absorption line in the broad H alpha emission line. Motivated by
an idea that this quasar may be a huge molecular gas reservoir in the early
phase of quasar evolution, we made CO(J=3-2) observations of it using the
Nobeyama Millimeter Array. No significant CO emission was detected; although an
emission-like feature (2.5 sigma) was seen close (~ 2") to the quasar, we
regard it as a noise. The obtained 3 sigma upper limit on the CO luminosity is
L'_{{\rm CO}(J=3-2)} = 4.5 \times 10^{10} K km/s pc^2, which corresponds to
M({\rm H}_2) = 3.6 times 10^10 M_{\odot} if we adopt the CO-to-H_2 conversion
factor of 0.8 M_{\odot} (K km/s pc^2)^{-1}. This upper limit is comparable to
L'_{{\rm CO}(J=3-2)} (and thus the molecular gas mass) detected in quasars and
BAL quasars at z=1-3, and no sign of the presence of the huge amount of
molecular gas in this FeLoBAL quasar was obtained.
