Chatter vibration is an undesired and indispensable phenomenon in turning operation, which cannot be completely avoided. However, it can be suppressed by early identification and with the proper choice of input turning parameters. The key issue of chatter detection is to process the acquired signals and extract the features pertaining to it. In the present work, a methodology has been proposed for exploring tool chatter features in the incipient stage during turning on lathe. Chatter signals generated during the turning of Al 6061-T6 have been acquired using a microphone. A stability lobe diagram has been plotted to access the stability regime. Further, in order to study the effect of feed rate on stability, the recorded signals have been processed using a local mean decomposition signal processing technique, followed by the selection of dominating product functions using the Fourier transform. The decomposed signals have been used to evaluate the new output parameter, that is, chatter index. Further, the Nakagami probability distribution has been used to ascertain stability region (threshold). From the experimental validation, it has been inferred that cutting combinations obtained from the Nakagami probability distribution are significant and capable of limiting chatter vibrations. The present methodology will serve as guidelines to the researchers and machinist for the identification of tool chatter in the incipient stage, explore its severity, and finally suppress it with the proper selection of input turning parameters.