Carrier-envelope phase (CEP) stabilization of a femtosecond chirped-pulse amplification system featuring a compact transmission grating compressor is demonstrated. The system includes two amplification stages and routinely generates phase-stable (approximately 250 mrad rms) 2 mJ, 25 fs pulses at 1 kHz. Minimizing the optical pathway in the compressor enables phase stabilization without feedback control of the grating separation or beam pointing. We also demonstrate for the first time to the best of our knowledge, out-of-loop control of the CEP using an acousto-optic programmable dispersive filter inside the laser chain.