The C-12/C-13, N-14/N-15, and S-32/S-34 isotope ratios in comet Hale-Bopp (C/1995 O1) were determined through observations taken with the James Clerk Maxwell Telescope, Measurements of rare isotopes in HCN and CS revealed isotope ratios of (HCN)-C-12/(HCN)-C-13 = 111 +/- 12, (HCN)-N-14/(HCN)-N-15 = 323 +/- 46, and (CS)-S-32/(CS)-S-34 = 27 +/- 3. Within the measurement uncertainties, the isotopic ratios are consistent with solar system values. The cometary volatiles thus have an origin in the solar system and show no evidence for an interstellar component.