Abstract: This work analyzes a phenomenon of self excited vibrations (mode coupling chatter) that was observed in a machine for wood cutting during the milling of a chair back. The configuration of the system for which chatter occurs is first illustrated. It is then recognized that the most crucial factor affecting the stability of the system is the angle g between the cutting force acting on the tool and one of the degrees of freedom of the structure. As a matter of fact, when g becomes smaller than a certain negative value, chatter occurs. An effective way to stabilize the milling machine is presented, consisting in changing the orientation of the tool with respect to the feed direction of the workpiece, so that the value of g is positive during the whole milling operation, and the instability zone is never entered. Tests carried out on the available milling machine proved the effectiveness of the stabilization. Finally, a theoretical framework is presented, which explains with more details how the stability of the system is affected by the value of g. Moreover, a simple stability condition which can be useful for practical stabilization purposes is also defined.