We produce a 3 mJ, two-cycle (11.4 fs), 1 kHz, carrier-envelope phase (CEP)-stable laser source at 1.7 μm via a three-stage Ti:sapphire-pumped optical parametric chirped-pulse amplifier in BiB3O6. We achieve a pump-to-signal conversion efficiency of 18% in the last stage, which is, to the best of our knowledge, the highest yet achieved for near-octave bandwidth amplification. A f-to-2f measurement shows a CEP instability of 165 mrad over 1 h. This is an ideal light source for generating isolated attosecond pulses in the soft x-ray region.