Regenerative chatter is known to be a key factor that limits the productivity of high speed machining. Consequently, a great deal of research has focused on developing predictive models of milling dynamics, to aid engineers involved in both research and manufacturing practice. Time-domain models suffer from being computationally intensive, particularly when they are used to predict the boundary of chatter stability, when a large number of simulation runs are required under different milling conditions. Furthermore, to identify the boundary of stability each simulation must run for sufficient time for the chatter effect to manifest itself in the numerical data, and this is a major contributor to the inefficiency of the chatter prediction process. In the present article, a new chatter criterion is proposed for time-domain milling simulations, that aims to overcome this drawback by considering the transient response of the modeled behavior, rather than the steady-state response. Using a series of numerical investigations, it is shown that in many cases the new criterion can enable the numerical prediction to be computed more than five times faster than was previously possible. In addition, the analysis yields greater detail concerning the nature of the chatter vibrations, and the degree of stability that is observed.