We demonstrate a chirped-pulse-amplified Ti:Sapphire laser system operating at 1 kHz, with 20 mJ pulse energy, 26 femtosecond pulse duration (0.77 terawatt), and excellent long term carrier-envelope-phase (CEP) stability. A new vibrational damping technique is implemented to significantly reduce vibrational noise on both the laser stretcher and compressor, thus enabling a single-shot CEP noise value of 250 mrad RMS over 1 hour and 300 mrad RMS over 9 hours. This is, to the best of our knowledge, the best long term CEP noise ever reported for any terawatt class laser. This laser is also used to pump a white-light-seeded optical parametric amplifier, producing 6 mJ of total energy in the signal and idler with 18 mJ of pumping energy. Due to preservation of the CEP in the white-light generated signal and passive CEP stability in the idler, this laser system promises synthesized laser pulses spanning multi-octaves of bandwidth at an unprecedented energy scale.