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The temporal distribution of the spectral parametric gain was experimentally investigated when a chirped pump pulse was injected into a photonic crystal fiber. A pump-probe experiment was developed and the important characteristics were measured as the chirp of the pump, the signal pulse, and the gain of the parametric amplifier. We highlight that the amplified spectrum depends strongly on the instantaneous pump wavelength and that the temporal evolution of the wavelength at maximum gain is not monotonic. This behavior is significantly different from the case in which the chirped pump has a constant peak power. This measurement will be very important to efficiently include parametric amplifiers in laser systems delivering ultra-short pulses.