We present extensive optical and infrared photometry of the afterglow ofgamma-ray burst (GRB) 030329 and its associated supernova (SN) 2003dhover the first two months after detection (2003 March 30-May 29 UT).Optical spectroscopy from a variety of telescopes is shown and, whencombined with the photometry, allows an unambiguous separation betweenthe afterglow and SN contributions. The optical afterglow of the GRB isinitially a power-law continuum but shows significant color variationsduring the first week that are unrelated to the presence of an SN. Theearly afterglow light curve also shows deviations from the typicalpower-law decay. An SN spectrum is first detectable ~7 days after theburst and dominates the light after ~11 days. The spectral evolution andthe light curve are shown to closely resemble those of SN 1998bw, apeculiar Type Ic SN associated with GRB 980425, and the time of the SNexplosion is close to the observed time of the GRB. It is now clear thatat least some GRBs arise from core-collapse SNe.