Female choice in various species of acoustic insects and anurans entails a psychoacoustic preference for male calls that lead their neighbors by a brief time interval. This discrimination, which can be termed a precedence effect, may select for various mechanisms with which males adjust call rhythm and thus reduce their incidence of ineffective following calls. At a collective level, alternating and synchronous choruses may emerge from these call timing mechanisms. Using playback experiments, we characterized the precedence effect in females of the katydid Ephippiger ephippiger, an alternating choruser in which males use a rhythm adjustment mechanism that prevents calling during brief intervals following their neighbors’ calls. E. ephippiger females oriented toward leading male calls in >75% of trials when relatively young (<40 d old) and when playbacks were timed so that following calls began within 100–250 ms of the leading ones. However, this preference declined to below 60% as females aged and the interval separating leading and following call onsets increased. The strength of this precedence effect varied greatly between females, but within broad age classes the effect in a given female was statistically repeatable. Such repeatability indicates the possibility that additive genetic variance could be a significant component of variation in the precedence effect. We discuss the implications of our findings and inference on genetic variance for evolution of the precedence effect and for chorusing.