We demonstrate a 1.2-GHz repetition rate, diode-pumped, self-starting, 168-fs (FWHM) pulsewidth Yb:KYW laser mode-locked by a carbon nanotube (CNT) saturable absorber mirror. To our knowledge, this result corresponds to the highest repetition rate from CNT-mode-locked femtosecond bulk solid-state lasers, reaching the GHz regime for the first time.