Disclosed herein is a derailleur for a chain bicycle designed to move forward with either forward or reverse rotation of the bicycle's pedals. The chain bicycle comprises a single endless chain, first and second rear wheel sprocket assemblies, first and second one-way clutches to transmit power to a rear wheel hub in only a forward direction, and an idler roller. Any one sprocket of the second rear wheel sprocket assembly engages with the endless chain by using a pantograph linkage, and at the same time, any one sprocket of the first rear wheel sprocket assembly engages with the endless chain by using a chain hook member. The idler roller is coupled to a second base member via a plurality of joint shafts, so as to permit not only rotating, tilting and sliding motions thereof relative to any one joint shaft, but also elastic pivotal rotation in either clockwise or counterclockwise direction relative to another joint shaft parallel to a pedal shaft.