Substantial power scaling of a travelling-wave femtosecond optical parametric amplifier, pumped near 800 nm by a 1 kHz Ti:sapphire laser amplifier, is demonstrated using monoclinic BiB3O6 in a two stage scheme with continuum seeding. Total energy output (signal plus idler) exceeding 1 mJ is achieved, corresponding to an intrinsic conversion efficiency of ≈32% for the second stage. The tunability extends from 1.1 to 2.9 μm. The high parametric gain and broad amplification bandwidth of this crystal allowed the maintenance of the pump pulse duration, leading to pulse lengths less than 140 fs, both for the signal and idler pulses, even at such high output levels.