A chain drive (1) comprises a chain (5) configured to rotate in a closed loop (6) forming a load track (7) and a return track (8) interconnected by first and second turnaround sections (9, 10); a drive sprocket (12) for driving the chain (5), the drive sprocket (12) being located in the first turnaround section (9) of the closed loop (6); and a polygon compensation system for compensating the polygon effect of the chain (5). At least one component (2, 4, 14, 26) of the polygon compensation system is located within at least one turnaround section (10) and/or in at least one of the load track (7) and the return track (8) .