Benefit from high flexibility, applicability and low cost of industrial robot, robotic drilling has found its way into the field of aviation manufacturing, improving both surface quality and drilling efficiency. However, an unexpected instability, known as chatter, commonly occurs during the robotic drilling process due to relatively insufficient stiffness of robotic joints. In this paper, a monitoring approach based on concentrated velocity synchronous linear chirplet transform is proposed for robotic drilling chatter. First, for the sake of eliminating spindle speed-related components from measured acceleration signals, an optimal notch filter is designed based on the least squares method. Further, to obtain smear-free and high-resolution time-frequency representation, an enhanced concentrated velocity synchronous linear chirplet transform (CVSLCT) is proposed to process the acceleration signals. Thereafter, the acceleration signals are compartmentalized into several bands of equal frequency width. By summing coefficients of CVSLCT, sub-signals corresponding to all the frequency bands could be reconstructed effectively. Taking into account inhomogeneous change of energy and frequency distribution for acceleration signal, energy entropy is computed at regular intervals and employed as chatter monitoring indicator. Eventually, the presented CVSLCT-based approach is verified experimentally via the established robotic drilling system and making comparisons with existing chatter monitoring methods. The results verify that the CVSLCT-based approach is capable of effectively recognizing robotic drilling chatter before its full development and is superior to the existing methods.