  The fluctuations of the longitudinal coherence length expected from the
world's first hard X-ray Free Electron Laser, the Linac Coherent Light Source,
are investigated. We analyze, on a shot-to-shot basis, series of power spectra
generated from 1D-FEL simulations. We evaluate how the intrinsic noise in the
spectral profile of the X-ray beam reflects on its longitudinal coherence
length. We show that the spectral stability of the LCLS beam will allow
coherent X-ray experiments with a reasonable acquisition time. We also propose
a scheme to deliver single-mode X-ray radiation using a narrow bandpass
monochromator.
