The article discusses the issues of determining contact stresses in the hinges of chain gears. It is necessary to know these stresses to assess the hinges’ wear resistance, since the wear of hinges (joints) is the most common cause of chain gears’ damage. In this regard, the focus was made on determining the necessary gap between the bushing and the roller of the chain gears. This gap significantly affects the largely determines the distribution pattern and magnitude of the stresses in the hinge, and, consequently, the wear resistance of chain gears. A method for calculating the maximum contact stress in the hinges of chain gears has been developed. It was proved that a decrease of the gap in the hinges influence in the following way: the contact angle between the roller and the bushing increases and the maximum contact stresses become lower. However, for real contact angles, the contact stresses greatly exceed the permissible average specific pressure, causing increased wear on the joints (hinges). One of the possible ways to solve this problem is to use transitional fittings in hinges, in which the gaps and tightness are relatively small. When pressing the rollers into the bushings, microroughnesses are cut from the contact surfaces, and the tightness in the connection practically disappears. Some examples of determining gaps and contact stresses in the hinges of chain gears are given.