Third-harmonic generation of high-intensity, sub-100-fs idler pulses from a Ti:sapphire-laser-pumped optical parametric amplifier is demonstrated by using a single nonlinear crystal of BiB₃O₆ (BIBO). Maximum internal energy conversion as high as 11% from the fundamental to the third harmonic is achieved by phase- and group-velocity matching for the direct cubic nonlinear process together with the velocity-mismatched cascading quadratic processes.