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 ( \sim 2 ^ { \prime \prime } ) to the quasar , we regard it as a noise . The obtained 3 \sigma upper limit on the CO luminosity is L ^ { \prime } _ { { CO } ( J = 3 - 2 ) } = 4.5 \times 10 ^ { 10 } K km s ^ { -1 } pc ^ { 2 } , which corresponds to M ( { 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 ^ { -1 } pc ^ { 2 } ) ^ { -1 } . This upper limit is comparable to L ^ { \prime } _ { { 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 .