  Atomic clocks have been transformational in science and technology, leading
to innovations such as global positioning, advanced communications, and tests
of fundamental constant variation. Next-generation optical atomic clocks can
extend the capability of these timekeepers, where researchers have long aspired
toward measurement precision at 1 part in $\bm{10^{18}}$. This milestone will
enable a second revolution of new timing applications such as relativistic
geodesy, enhanced Earth- and space-based navigation and telescopy, and new
tests on physics beyond the Standard Model. Here, we describe the development
and operation of two optical lattice clocks, both utilizing spin-polarized,
ultracold atomic ytterbium. A measurement comparing these systems demonstrates
an unprecedented atomic clock instability of $\bm{1.6\times 10^{-18}}$ after
only $\bm{7}$ hours of averaging.
