A bicycle rear derailleur has a base member mountable to a bicycle frame, a movable member movably coupled to the base member, a chain guide assembly rotatably connected to the movable member for rotation about a rotational axis, a biasing element configured and arranged to bias the chain guide assembly for rotation in a first rotational direction with respect to the movable member, and a fluid damper having a fluid cavity containing a volume of fluid. The fluid damper is operatively disposed between the chain guide assembly and the movable member to apply a damping force to the chain guide assembly when the chain guide assembly rotates in a second rotational direction opposite to the first rotational direction. The fluid damper has a guide wheel configured to route a chain and rotatable about the rotational axis.