  Thermally induced fluctuations impose a fundamental limit on precision
measurement. In optical interferometry, the current bounds of stability and
sensitivity are dictated by the excess mechanical damping of the
high-reflectivity coatings that comprise the cavity end mirrors. Over the
preceding decade, the mechanical loss of these amorphous multilayer reflectors
has at best been reduced by a factor of two. Here we demonstrate a new paradigm
in optical coating technology based on direct-bonded monocrystalline
multilayers, which exhibit both intrinsically low mechanical loss and high
optical quality. Employing these "crystalline coatings" as end mirrors in a
Fabry-P\'erot cavity, we obtain a finesse of 150,000. More importantly, at room
temperature, we observe a thermally-limited noise floor consistent with a
tenfold reduction in mechanical damping when compared with the best dielectric
multilayers. These results pave the way for the next generation of
ultra-sensitive interferometers, as well as for new levels of laser stability.
