Laser-cooled sodium atoms pushed up on a vertical trajectory by radiation pressure are observed to turn around due to gravity. The reatively long time the atoms spent freely falling in this atomic fountain allowed the ground-state hyperfine splitting to be measured with a linewidth of 2 Hz. After a 1000-s integration time, the center of the line was resolved to ±10 mHz. The absolute splitting was measured to be 1 771 626 129(2) Hz. © 1989 The American Physical Society.