Chain transmissions are widespread in drives of machines used for various industrial purposes. In order to study drive dynamics, it is important to know the dissipative characteristics of its components and gears. However, the information on the damping ability of chain transmissions in research and technical literature is limited and fragmented, which makes the topic of this work, dedicated to the study of energy dissipation in transverse vibrations of chain transmission branches, of great current interest. The objective of this work was to study and determine the quantitative characteristics of energy dissipation in a drive chain experiencing the most common form of transverse vibrations as a string with fixed ends, which is characteristic of transmissions with large masses of sprockets and parts attached to them. To achieve this objective, a mathematical model of the dissipation of vibrational energy was developed using a method of estimating energy losses due to friction when parts of the chain’s hinge joint slip in a compressed contact. Engineering formulas for calculating energy dissipation per cycle of vibrations and absorption coefficient were obtained. The adequacy of the developed model and the obtained calculation formulas was confirmed by the results of the experimental determination of the absorption coefficients of the chain using the method of free damped vibrations. The results of the study allow us to conclude that chain transmissions have an increased damping capacity, and to determine the influence of transmission parameters and the oscillatory process on it.