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.
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