  Many atomic and molecular systems of fundamental interest possess resonance
frequencies in the extreme ultraviolet (XUV) where laser technology is limited
and radiation sources have traditionally lacked long-term phase coherence.
Recent breakthroughs in XUV frequency comb technology have demonstrated
spectroscopy with unprecedented resolution at the megahertz level, but even
higher resolutions are desired for future applications in precision
measurement. By characterizing heterodyne beats between two XUV comb sources,
we demonstrate the capability for sub-hertz spectral resolution. This
corresponds to coherence times >1 s at photon energies up to 20 eV, more than
six orders of magnitude longer than previously reported. This work establishes
the ability of creating highly phase-stable radiation in the XUV with
performance rivaling that of visible light. Furthermore, by direct sampling of
the phase of the XUV light originating from high-harmonic generation, we
demonstrate precise measurements of attosecond strong-field physics.
