The first lifetime measurements have been performed for six levels of doubly ionized thorium, an important cosmochronometer in astrophysics for estimating the age of the Galaxy. The levels, belonging to the 5f2, 5f7p, 7s7p, and 6d7p configurations of Th III, have been measured by the time-resolved laser-induced fluorescence method and compared with relativistic Hartree-Fock calculations including configuration interaction and core-polarization effects. Taking advantage of the excellent agreement between theory and experiment, a first set of transition probabilities of astrophysical interest has been deduced for this ion from a combination of the experimental lifetimes and of the theoretical branching fractions.