An experiment was performed at Lawrence Berkeley National Laboratory's 88-in. Cyclotron to determine the mass number of a superheavy element. The measurement resulted in the observation of two α-decay chains, produced via the ^{243}Am(^{48}Ca,xn)^{291-x}Mc reaction, that were separated by mass-to-charge ratio (A/q) and identified by the combined BGS+FIONA apparatus. One event occurred at A/q=284 and was assigned to ^{284}Nh (Z=113), the α-decay daughter of ^{288}Mc (Z=115), while the second occurred at A/q=288 and was assigned to ^{288}Mc. This experiment represents the first direct measurements of the mass numbers of superheavy elements, confirming previous (indirect) mass-number assignments.