A saw chain has pivotally interconnected chain links which includes cutting links and safety links and these links are effective as working links. The cutting links are each provided with a cutting tooth for cutting into wood and the safety links are each provided with a projection which limits the depth of the cut of the cutting tooth which follows the safety link. The pivot axes of the chain links lie in an action plane above the guide bar in the stretched portion of the saw chain when the latter is subjected to the pulling force exerted by the drive of the chain saw. The cutting links are pivotable with respect to this plane. In addition, the safety links can also be pivotable in this manner. When the cutting links are in their pivoted-out position under this pulling force, no clearance angle is available at the roof of the cutting tooth so that the cutting edge has no cutting effect. For this reason, there is no kickback when the saw chain is placed against the wood. When an advancing thrust is applied to the chain saw, the cutting links in the stretched running portion of the chain are pivoted into their pivoted back position or working position by means of reaction forces; whereas, in the direction-reversal region of the guide bar, the cutting links are retained in their pivoted-out position by means of the support imparted to the drive links by the nose sprocket of the guide bar. In this way, the danger of kickback remains low.