X-ray free-electron lasers deliver intense femtosecond pulses that promise to yield high resolution diffraction data of nanocrystals before the destruction of the sample by radiation damage. Diffraction intensities of lysozyme nanocrystals collected at the Linac Coherent Light Source using 2 keV photons were used for structure determination by molecular replacement and analyzed for radiation damage as a function of pulse length and fluence. Signatures of radiation damage are observed for pulses as short as 70 fs. Parametric scaling used in conventional crystallography does not account for the observed effects.