Atomic clocks have been instrumental in science and technology, leading to innovations such as global positioning, advanced communications, and tests of fundamental constant variation. Timekeeping precision at 1 part in 10(18) enables new timing applications in relativistic geodesy, enhanced Earth- and space-based navigation and telescopy, and new tests of physics beyond the standard model. Here, we describe the development and operation of two optical lattice clocks, both using spin-polarized, ultracold atomic ytterbium. A measurement comparing these systems demonstrates an unprecedented atomic clock instability of 1.6 x 10(-18) after only 7 hours of averaging.