The complex molecules vinyl cyanide (CH2CHCN), methyl formate (HCOOCH3), and ethyl cyanide (CH3CH2CN) were observed in the Sgr B2 star-forming region with the BIMA millimeter wavelength array. A region with diameter less than 0.1 pc toward the Sgr B2(N) molecular core is found to be the major source of these molecules. Also, this source is coincident with continuum emission from dust and a center of H2O maser activity. Ultracompact (UC) H 11 regions are located within 0.1 pc. Strikingly, none of these molecules is detected toward Sgr B2(M), a core located 1 minute south of Sgr B2(N). The existence of complex molecules, a large mass of dust, high-velocity H2O masers, and UC H 11 regions strongly suggests that the Sgr B2(N) region has just begun to form stars, while the absence of strong dust emission and large molecules suggests Sgr B2(M) is more evolved. The detection of large molecules coincident with continuum emission from dust supports the idea found in current chemical models that grain chemistry is of crucial importance for the formation of these molecules.