We present the Spitzer/IRS mid-infrared spectrum of the infrared-luminous (L_(IR) = 4 × 10^(11) L_☉) brightest cluster galaxy (BCG) in the X-ray-luminous cluster Zwicky 3146 (Z3146; z = 0.29). The spectrum shows strong aromatic emission features, indicating that the dominant source of the infrared luminosity is star formation. The most striking feature of the spectrum, however, is the exceptionally strong molecular hydrogen (H_2) emission lines, which seem to be shock-excited. The line luminosities and inferred warm H_2 gas mass (~10^(10) M_☉) are 6 times larger than those of NGC 6240, the most H_2-luminous galaxy at z ≲ 0.05. Together with the large amount of cold H_2 detected previously (~10^(11) M_☉), this indicates that the Z3146 BCG contains disproportionately large amounts of both warm and cold H_2 gas for its infrared luminosity, which may be related to the intracluster gas cooling process in the cluster core
