We have studied both theoretically and experimentally a new scheme of active pulse compression in a free electron laser (FEL) amplifier. The pulse compression scheme presented here is the following. A frequency-chirped pulse is injected into the FEL interaction region. Because of the high gain and narrow bandwidth of the FEL interaction, only the resonant frequency band of the pulse is actively amplified, resulting in a short pulse of high power coherent radiation at the output of the laser. For our experimental parameters (beam voltage ∼ 150 kV, current ∼ 5.0 A, wiggler period ⋍ 3.5 cm and gain ∼ 10 dB), pulses of a few nanoseconds were generated at ⋍ 10 GHz after an interaction length of 2.30 m, in good agreement with theoretical expectations. For the same input pulses (width > 100 ns, frequency chirp α2π ∼ 5 MHz/ns), the obtention of such compression ratios would require hundreds of meters of dispersive medium (waveguide, for example), with prohibitively high attenuations. These experimental result represent what we believe to be the first measurements of FM effects in an FEL amplifier.