A femtosecond optical frequency comb and continuous-wave pulse-amplified laser were used to measure 12 transition frequencies of antiprotonic helium (metastable three-body system consisting of an antiproton, an electron, and a helium nucleus) to fractional precisions of (9–16) × 10^–9. One of these is between two states having microsecond-scale lifetimes hitherto unaccessible to our precision laser spectroscopy method. Comparisons with three-body QED calculations yielded an antiproton-to-electron mass ratio of  = 1836.152 674(5).PACS Nos.: 36.10.–k, 14.20.Dh, 32.70.Jz