When the afterglow fades at the site of a long-duration gamma-ray burst (LGRB), Type Ic supernovae (SN Ic) are the only type of core collapse supernova observed. Recent work found that a sample of LGRB in high-redshift galaxies had different environments from a collection of core-collapse environments, which were identified from their colors and light curves. LGRB were in the brightest regions of their hosts, but the core-collapse sample followed the overall distribution of the galaxy light. Here we examine 504 supernovae with types assigned based on their spectra that are located in nearby (z < 0.06) galaxies for which we have constructed surface photometry from the Sloan Digital Sky Survey (SDSS). The distributions of the thermonuclear supernovae (SN Ia) and some varieties of core-collapse supernovae (SN II and SN Ib) follow the galaxy light, but the SN Ic (like LGRB) are much more likely to erupt in the brightest regions of their hosts. The high-redshift hosts of LGRB are overwhelmingly irregulars, without bulges, while many low redshift SN Ic hosts are spirals with small bulges. When we remove the bulge light from our low-redshift sample, the SN Ic and LGRB distributions agree extremely well. If both LGRB and SN Ic stem from very massive stars, then it seems plausible that the conditions necessary for forming SN Ic are also required for LGRB. Additional factors, including metallicity, may determine whether the stellar evolution of a massive star leads to a LGRB with an underlying broad-lined SN Ic, or simply a SN Ic without a gamma-ray burst.