  We demonstrate Ramsey-Bord\'e (RB) atom interferometry for high performance
laser stabilization with fractional frequency instability $<2 \times 10^{-16}$
for timescales between 10 and 1000s. The RB spectroscopy laser interrogates two
counterpropagating $^{40}$Ca beams on the $^1$S$_0$ -- $^3$P$_1$ transition at
657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detection
of the excited state population is performed on the (4s4p) $^3$P$_1$ --
(4p$^2$) $^3$P$_0$ transition at 431 nm. Minimal thermal shielding and no
vibration isolation are used. These stability results surpass performance from
other thermal atomic or molecular systems by one to two orders of magnitude,
and further improvements look feasible.
