We present the first carrier-envelope-phase stable chirped-pulse amplifier (CPA) featuring high temporal contrast for relativistic intensity laser-plasma interactions at 1 kHz repetition rate. The laser is based on a double-CPA architecture including cross-polarized wave (XPW) filtering technique and a high-energy grism-based compressor. The 8 mJ, 22 fs pulses feature 10⁻¹¹ temporal contrast at -20 ps and a carrier-envelope-phase drift of 240 mrad root mean square.