We generate linearly polarized, 287 W average-power, 5.5 ps pulses using a cryogenically cooled Yb:YAG amplifier at a repetition rate of 78 MHz. An optical-to-optical efficiency of 41% is obtained at 700 W pump power. A 6 W, 0.4 nm bandwidth picosecond seed source at 1029 nm wavelength is constructed using a chirped-pulse fiber amplification chain based on chirped volume Bragg gratings. The combination of a fiber amplifier system and a cryogenically cooled Yb:YAG amplifier results in good spatial beam quality at large average power. Low nonlinear phase accumulation as small as 5.1 x 10(-3) rad in the bulk Yb:YAG amplifier supports power scalability to a > 10 kW level without being affected by self-phase modulation. This amplification system is well suited for pumping high-power high-repetition-rate optical parametric chirped-pulse amplifiers.