An apparatus for providing exercise to recreational users and training to professional users comprising a support frame on which a bicycle frame is mounted and a resistance generation unit coupled to the support frame to provide resistance against the pedalingof the user. The resistance unit comprises a magnetic field generation source and a flywheel having an annular ring constructed from a plurality of segments of a non-magnetic, conductive material. The resistance exercise apparatus and trainer utilizes the flywheel to eliminate the need for the conventional rear wheel of a bicycle. The use of the flywheel as part of the resistance generation unit creates a "single-stage" resistance exercise trainer, because the resistance generated on the flywheel is transmitted to the user through a direct chain drive of a conventional bicycle. According to another aspect of the present invention, the resistance exercise apparatus includes a chain tensioning mechanism. The chain tensioning mechanism provides a method of tightening or loosenig the tension of the chain to improve the overall efficiencyof the chain drive mechanism and prevent the chain from "jumping"off the chain ring during operation.