By seeding an optical-field-ionized population inverted plasma amplifier with the 25th harmonic of an infrared laser we have produced a compact, diffraction- limited and Fourier-limited laser beam in the soft x-ray spectral range. This laser beam is emitted within a cone of 0.7 mrad at a repetition rate of 10 Hz at a central wavelength of 32.8 nm, The beam exhibits a regular Gaussian spatial profile, and wavefront distortions smaller than λ/17. The measured coherence time of 5.5 ps is equal to the duration of the lifetime of the amplifying plasma which shows that this source has reached the Fourier limit.