This is the accepted manuscript made available via CHORUS. The article has been published as: Single-Ion Nuclear Clock for Metrology at the 19th Decimal Place C. J. Campbell, A. G. Radnaev, A. Kuzmich, V. A. Dzuba, V. V. Flambaum, and A. Derevianko Phys. Rev. Lett. 108, 120802 — Published 22 March 2012 DOI: 10.1103/PhysRevLett.108.120802