A chain tensioner (50; 500) for a conveying device (70) of a machine (1; 1′) for processing elements in the form of sheets (10), the conveying device (70) includes two lateral chain sets connected to the ends of transverse gripper bars (75) able to grasp the elements (10) and at least one chain-guiding device (90) configured to guide a respective chain set (80); the chain tensioner (50; 500) includes: an actuator (9) controlled by a control unit (8), a movable support (11), a transmission element (12) borne by the movable support (11), a rotary element (13) rotated by the actuator (9) and cooperating with the transmission element (12) in order to exert a thrust force on the movable support (11), the rotary element (13) being rotatable, to adjust the tension of the chain set (80). The actuator (9) is controlled in synchronism with the machine angle (MA). A machine (1; 1′) for processing elements and a method for tensioning the chain sets (80) of the conveying device (70) are disclosed.