For the past 50 years, atomic standards based on the frequency of the cesium ground-state hyperfine transition have been the most accurate time pieces in the world. We now report a comparison between the cesium fountain standard NIST-F1, which has been evaluated with an inaccuracy of about 4 x 10(-16), and an optical frequency standard based on an ultraviolet transition in a single, laser-cooled mercury ion for which the fractional systematic frequency uncertainty was below 7.2 x 10(-17). The absolute frequency of the transition was measured versus cesium to be 1,064,721,609,899,144.94 (97) Hz, with a statistically limited total fractional uncertainty of 9.1 x 10(-16) the most accurate absolute measurement of an optical frequency to date.