High-frequency band-pass filtering of acceleration records from the 1999 Chi-Chi, Taiwan, earthquake (Mw 7.6) resolves the continuous signal into a series of relatively short-duration discrete-energy bursts. We hypothesize that these bursts originate near the individual stations as small, shallow events that have been dynamically triggered by the P and S waves generated by the Chi-Chi mainshock; however, we cannot rule out the possibility that they originate from some nonseismic source associated with the surface, such as buildings or trees. Bursts are observed only during the seismic signal and not in the pre- or postsignal noise. The bursts are not likely to be generated by the instruments because groupings of three colocated individual instruments record identical bursts. Also, we show that the bursts are not due to the band-pass filtering of instrumentally generated step functions. The hypothesis that they are local events is supported by the observation of bursts in the 40-Hz frequency band at distances up to 170 km from the epicenter. If the bursts originated on the Chi-Chi fault plane, as hypothesized by Chen et al. (2006), based on their analysis of recordings within 20 km from the Chelungpu fault, then they should not be observable at this distance, assuming any reasonable value of crustal attenuation. Assuming a local origin, we estimate an average local event magnitude of Mw 0.2 and a source-receiver distance of approximately 1 km. We extended our analysis to lower stress levels by analyzing records from a smaller (Mw 5.3) event that was recorded by many of the same instruments used in the Chi-Chi analysis. For this event, bursts are observed only on the accelerograms from stations relatively close to the mainshock hypocenter. Analysis of the combined data set from both mainshocks suggests a stress threshold for triggering in the range 0.03–0.05 Mpa for S-wave triggering and 0.0013–0.0033 Mpa for P-wave triggering, consistent with prior observations of surface-wave triggering.