The chaotic dynamics of a crack-containing gear transmission system were analyzed, and a chaotic control strategy was proposed. Firstly, a model of a crack-containing three-degree-of-freedom gear system was established to analyze the effect of crack evolution on meshing stiffness. Subsequently, the change rule of the system dynamics response under the action of parameter ω-ξ coupling was analyzed. The distribution map of motion on the parameter plane of the system, the displacement amplitude cloud map, and so on were drawn. The correlation between chaotic motions and specific parameter conditions of the system and the characteristics of their manifestation were analyzed. Secondly, the law of the coexistence of attractors was investigated through the multi-primary-value bifurcation map. Aiming at the region where chaos occurred in some parameter intervals, a chaotic controller was designed based on Extreme Learning Machine (ELM). A control performance index function was constructed to control the chaotic motion into the expected periodic motion by using the output of the chaotic controller to output tiny perturbations applied to the controllable parameters ω and ξ of the system. Meanwhile, the Elite Selection Strategy Slime Mould Algorithm (ESMA) was combined with ELM to optimize the parameters of the chaotic controller. Additionally, based on the attractor coexistence law, the system was stabilized to a periodic orbit with a smaller displacement amplitude by force feedback control. Finally the effectiveness of the proposed control strategy was ultimately verified by simulation.