We report a novel implementation of chirped-pulse amplification (CPA) by dominantly using dispersive multilayer mirrors for chirp control. Our prototyp dispersive-mirror (DMC) compressor has been designed for a kHz Ti:sapphire amplifier and yielded--in a proof-of-concept study--millijoule-energy, sub-20-fs, 790-nm laser pulses with an overall throughput of approximately 90% and unprecedented spatio-temporal quality. Dispersive-mirror-based CPA permits a dramatic simplification of high-power lasers and affords promise for their advancement to shorter pulse durations, higher peak powers, and higher average powers with user-friendly systems.