The double-beta beta beta(2 nu)-decay rate of 100Mo to the first excited 0(+) state of 100Ru has been measured by a gamma-gamma coincidence technique that uses two HPGe detectors to observe the two gamma rays ( E(gamma 1) = 590.76 keV; E(gamma 2) = 539.53 keV) from the 100Ru nucleus as it deexcites to the ground state via the 0(+)-->2(+)-->0(+) sequence. Unlike all previous beta beta-decay experiments, this technique provides data which have a large signal-to-background ratio. After a 440-day measurement of a 1.05-kg isotopically enriched (98.4%) disk of 100Mo, 22 detected coincidence events (with an estimated background of 2.5 events) yield a half-life of [5.9(+1.7)(-1.1)(stat)+/-0.6(syst)] x 10(20) years.