We report the imaging and spectroscopic localization of GRB 060218 to a low-metallicity dwarf starburst galaxy at z = 0.03345 c 0.00006. In addition to making it the second nearest gamma-ray burst known, optical spectroscopy reveals the earliest detection of weak, supernova-like Si II near 5720 A (60.1c), starting 1.95 days after the burst trigger. UBVRIphotometry obtained between 1 and 26 days postburst confirms the early rise of supernova light, and suggests a short time delay between the gamma-ray burst and the onset of SN 2006aj if the early appearance of a soft component in the X-ray spectrum is understood as a "shock breakout." Together, these results verify the long-hypothesized origin of soft gamma-ray bursts in the deaths of massive stars.