We have measured the superconducting transition temperature Tc of Ni/Nb/Ni trilayers when the magnetizations of the two outer Ni layers are parallel (P) and antiparallel (AP). The largest difference in occurs when the Nb thickness is just above the critical thickness at which superconductivity disappears completely. We have observed a difference in Tc between the P and AP states as large as 41 mK--a significant increase over earlier results in samples with higher Tc and with a CuNi alloy in place of the Ni. Our result also demonstrates that strong elemental ferromagnets are promising candidates for future investigations of ferromagnet/superconductor heterostructures.