  We present a laser source delivering waveform-controlled 1.5-cycle pulses
that can be focused to relativistic intensity at 1 kHz repetition rate. These
pulses are generated by nonlinear compression of high-temporal-contrast
sub-25\,fs pulses from a kHz Ti:Sapphire double-chirped pulse amplifier in a
stretched flexible hollow fiber compressor scaled for high peak power. The
unique capabilities of this source are demonstrated by observing
carrier-envelope phase effects in laser-wakefield acceleration of relativistic
electrons for the first time.
