Femtosecond laser pulses enable the synthesis of light across the electromagnetic spectrum and provide access to ultrafast phenomena in physics, biology, and chemistry. Chip-integration of femtosecond technology could revolutionize applications such as point-of-care diagnostics, bio-medical imaging, portable chemical sensing, or autonomous navigation. However, current chip-integrated pulse sources lack the required peak power, and on-chip amplification of femtosecond pulses has been an unresolved challenge. Here, addressing this challenge, we report >50-fold amplification of 1 GHz-repetition-rate chirped femtosecond pulses in a CMOS-compatible photonic chip to 800 W peak power with 116 fs pulse duration. This power level is 2–3 orders of magnitude higher compared to those in previously demonstrated on-chip pulse sources and can provide the power needed to address key applications. To achieve this, detrimental nonlinear effects are mitigated through all-normal dispersion, large mode-area and rare-earth-doped gain waveguides. These results offer a pathway to chip-integrated femtosecond technology with peak power levels characteristic of table-top sources.