We report an experimental/theoretical study of single-crystal Bi(2)Ir(2)O(7) that possesses a metallic state with strongly exchange-enhanced paramagnetism. The ground state of Bi(2)Ir(2)O(7) is characterized by the following features: (1) a divergent low-temperature magnetic susceptibility that indicates no long-range order down to 50 mK; (2) strongly field-dependent coefficients of the low-temperature T and T(3) terms of the specific heat; (3) a conspicuously large Wilson ratio R(W) ≈ 53.5; and (4) unusual temperature and field dependences of the Hall resistivity that abruptly change below 80 K, without any clear correlation with the magnetic behavior. All these unconventional properties suggest the existence of an exotic ground state in Bi(2)Ir(2)O(7).