PURPOSE: To provide a chain-turning system capable of turning a chain having a link of a prescribed length in a far smaller turning radius concerning the same polygonal effect, since the polygonal effect is smaller than that in the chain turning system of a conventional technique.

CONSTITUTION: A chain turning system has at least one transition curve (UK.11, UK.12) that joins up with the circular turning arc (B.11) in order to reduce the polygonal effect. The radius of curvature of the transition curve varies continuously. The transition curve desirably joins up with a straight portion (G.11, G.12) of the chain's track or to another turning arc. It is desirable that in the transmission curve the radius of the curvature at its junction (A.11, A.12) with the turning arc (B.11) is the same as the turning radius, and the radius of the curvature at its junctions (C.11, C.12) with the straight portions (G.11, G.12) of the chain's track are a part of an infinitely large clothoid.