As product quality and production capacity requirements for precision processing become higher, making machine tools smart and improving performance is becoming the trend. In terms of machine tool processing quality, tool wear and chatter vibration are the factors that most directly affect processing quality. Traditionally, operators rely on their experience in determining whether the tool is worn or if there is chatter vibration. However, experience is not quantified data. Experience does not have a uniform judgment standard and can easily lead to wrong judgment. In recent years, many scholars have conducted in-depth studies of the two aforementioned phenomenons. These studies mainly use time and frequency domains to search for phenomenon features as the determination basis. Of time and frequency domain, studies on frequency domain are the most common. However, the frequency domain method requires a large amount of calculation, and the analysis process requires an excessive quantity of data dimensions, making this method unsuitable for real-time analysis. Thus, we propose a general regression neural network analysis method based on Chua's circuit and a fractional-order Lorenz master/slave composite chaotic system for detecting lathe tool turning chatter vibration in this study. We compared the dynamic error features produced by various fractionalorder chaotic systems and chose fractional orders with more obvious feature changes. We then substituted general regression neural network categorization. Compared to the frequency domain analysis method, the method proposed in this study requires fewer data dimensions, fewer calculations, and higher efficiency. Our proposed method also has higher precision and a higher discrimination rate. The result of this study shows that our proposed method has a 100% discrimination rate for determining turning chatter vibration.