We present Hubble Space Telescope Hα and [S II] images of HH 29. The proximity of HH 29 (140 pc) and the high resolution of the Planetary Camera has resulted in the most detailed images obtained so far of any Herbig-Haro object. The most prominent feature is a linear Hα ridge leading the working surface of a bow shock with a chaotic trailing [S II] bright region. The high-excitation ridge is perpendicular to a line extending toward the class 0 protostar L1551-NE, supporting its recent identification as the driving source. Previous studies have identified several low-velocity features within the working surface. Our images reveal them to be miniature bow shocks facing upstream. Evidently a cluster of dense quasi-stationary clumps have been overrun by a faster, lower density flow. The shock front impacted the front of the largest clump several decades ago, and during the 1990s, a prominent gap appeared in the advancing bow shock in the wake of the obstacle. The Hubble Space Telescope images show that by 1998 the shock front had wrapped around the back of the clump, closing the shock shadow it produced.