Forty-seven graphite round grains from the lowest density fraction extracted from the Murchison carbonaceous chondrite were analyzed for their C and N isotopic ratios by ion microprobe mass spectrometry, and subsets of the grains were analyzed for their O, Mg, Si, Ca, and Ti isotopic ratios. The C-12/C-13 ratios of the grains range from 6.3 to 3140 (solar ratio is 89). Most grains have N-15 excesses (up to 2.5 times solar), O-18 excesses (up to 100 times solar), and large inferred Al-26/Al-27 ratios (up to 0.15), and Si isotopic compositions range from Si-28 excesses (up to 30%) to Si-29 and Si-30 excesses (up to 50%). All seven grains analyzed for Ti show large Ti-49 excesses (up to 170%), and some show Ca-42 and Ca-43 excesses and Mg-25 excesses. The large O-18 excesses point to an origin in massive stars, either Wolf-Rayet stars or Type II supernovae, where O-18 is produced from N-14 at the onset of He burning. Most of the other isotopic signatures are consistent with such an origin: the Ti, Ca, and Mg anomalies can be explained by slow neutron capture during He burning, the large Al-26/Al-27 ratios by admixture of material that has experienced H burning. The large variations in the Si isotopic compositions, including both Si-29 and Si-30 excesses and deficits, favor a supernova origin with Si-28 coming from oxygen burning in an inner layer of the star.