By analyzing published geochemical data on xenon isotopes measured in a 2.46 x 10(9)-year-old telluride ore, a lower limit of 1.6 x 10(25) years has been obtained for the mean lifetime of the nucleons in the tellurium-130 nucleus. This result is insensitive to the particular mode by which the nucleons decay and therefore provides a rigorous limit on possible baryon number nonconservation. The new limit is about two orders of magnitude better than the previous rigorous limit on nucleon stability.