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This paper presents new images and spectroscopy of NGC 34 (Mrk 938) obtained with the du Pont 2.5-m and Baade 6.5-m telescopes at Las Campanas, plus photometry of an HST archival V image. This Mv = -21.6 galaxy has often been classified as a Seyfert 2, yet recently published infrared spectra suggest a dominant central starburst. We find that the galaxy features a single nucleus, a main spheroid containing a blue central disk, and tidal tails indicative of two former disk galaxies. These galaxies appear to have completed merging. The remnant shows three clear optical signs that the merger was gas-rich ("wet") and accompanied by a starburst: (1) It sports a rich system of young star clusters, of which 87 have absolute magnitudes -10.0 > Mv > -15.4. Five clusters with available spectra have ages in the range 0.1-1.0 Gyr, photometric masses between 2x10^6 and 2x10^7 Msun, and are gravitationally bound young globulars. (2) The blue central disk appears to be ...