A chain damping and shock absorber system for a chain includes one or more damping devices, each damping device installed to a segment of the chain, such that the chain and the one or more damping devices installed to a chain segment form a damped and compressed chain assembly. In response to a tensile force applied to the chain, the chain segment is extendable to an extended length which is between its compressed length and its full length. Methods of installing the chain damping and shock absorber system are provided.