We describe a few-cycle intense optical parametric chirped pulse amplifier (OPCPA) in the IR that is based on bismuth triborate (BiB3O6, BIBO) crystals. Two Ti:sapphire chirped pulse amplification systems are used to generate seed and pump pulses for the OPCPA. Carrier-envelope phase (CEP)-stabilized seed pulses in the IR are produced by difference frequency mixing of white light spanning from the visible to near IR range. The seed pulses, which have a nearly one octave-spanning spectrum around 1.6 μm, are temporally stretched in an acousto-optic programmable dispersive filter and amplified up to 550 μJ in two BIBO-based parametric amplifiers without losing their bandwidth. After compression in a fused silica block, we obtained 9.2 fs optical pulses with a repetition rate of 1 kHz, which comprise less than two optical cycles at 1.6 μm. These optical pulses were used to generate extreme ultraviolet (XUV) high harmonics in krypton. We succeeded in measuring the CEP dependence of the XUV radiation near the silicon L edge around 100 eV, verifying the passive stabilization of the CEP of the sub-two cycle IR pulses. The XUV spectra consist of two half-cycle cutoffs and show a clear transition from a modulated structure to a continuum near the cutoff. The continuum-like spectra as well as their CEP dependence indicate that they originate in a single recombination burst, showing that few-cycle IR OPCPA light sources are capable of generating attosecond pulses in the XUV region.