The Soft Gamma Repeater SGR 1900+14 entered a remarkable phase of activity during the summer of 1998. This activity peaked on August 27, 1998 when a giant periodic gamma-ray flare resembling the famous March 5, 1979 event from SGR 0526-66 was recorded. Two days later (August 29), a strong, bright burst was detected with RXTE and BATSE. This event reveals several similarities to the giant flares of August 27 and March 5, and shows a number of unique features not previously seen in SGR bursts. Unlike typically short SGR bursts, this event features a 3.5 s burst peak that was preceded by an extended (~ 1 s) complex precursor, and followed by a long (~ 1000 s) periodic tail modulated at the 5.16 s stellar rotation period. Spectral analysis shows a striking distinction between the spectral behavior of the precursor, burst peak and extended tail. While the spectrum during the peak is uniform, a significant spectral evolution is detected in both the precursor and tail emissions. Temporal behavior shows a sharp rise (~ 9.8 ms) at the event onset and a rapid cutoff (~ 17 ms) at the end of the burst peak. The tail pulsations show a simple pulse profile consisting of one 5.16 s peak that did not evolve with time. The spectral and temporal signatures of this event imply that the precursor, main peak, and extended tail are produced by different physical mechanisms. We discuss these features and their implications in the context of the magnetar model. The energetics of the August 29 event, and its close proximity to the August 27 flare, suggest that it is an `aftershock of the preceding giant flare. P.S. This is an abbreviated version of the original abstract.