High field science relies on ultrashort pulse lasers with multi-joule pulse energies for studying light–matter interactions under extreme conditions and for driving particle accelerators and secondary radiation sources of x rays, gamma rays, neutrons, positrons, muons, and protons. Next-generation laser drivers will require a 103−104 times increase in pulse repetition rates, producing multi-joule energies at multi-kilowatt average powers to enable practical applications in nuclear engineering, advanced materials, medicine, biology, homeland security, and high-energy physics. Spatially coherently combined femtosecond fiber lasers are recognized as a pathway to these next-generation drivers, with significant practical advantages including high efficiency and the possibility of compact integration. However, chirped pulse amplification in fibers is capable of extracting only a small fraction (usually ∼1%) of the maximum stored energy. Here we demonstrate near-complete maximum stored energy extraction with low accumulated nonlinearity from a large-core fiber amplifier using coherent pulse stacking amplification. We have amplified a 81-pulse stacking burst in a 85 µm core chirally coupled core Yb-doped fiber, extracting up to 9.5 mJ (∼90% of stored energy) with <4.5 radians of accumulated nonlinear phase, temporally combined this burst into a single pulse, and achieved 4.2 mJ pulses of 313 fs bandwidth-limited duration after compression. This represents, to our knowledge, the highest energy extracted and compressed into a femtosecond pulse from a single fiber amplifier, enabling approximately two orders of magnitude size reduction of future high-energy coherently spatially combined fiber laser arrays.