The spatial coherence of free-electron laser radiation in the water window spectral range was studied, using the third harmonic (λ₃=2.66 nm) of DESY's Free-electron LASer in Hamburg (FLASH). Coherent single pulse diffraction patterns of 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) multilamellar lipid stacks have been recorded. The intensity histogram of the speckle pattern around the first lamellar Bragg peak, corresponding to the d=5 nm periodicity of the stack, reveals an average number of transverse modes of M̄=3.0 of the 3rd harmonic. Using the lipid stack as a “monochromator”, pulse-to-pulse fluctuations in the third harmonic λ₃ have been determined to be 0.033 nm.