A gamma ray spectrometer at LBNL (the Luis W. Alvarez Iridium Coincidence Spectrometer), that was specifically designed for high sensitivity measurements of iridium abundances, has been significantly modified in order to provide precisions of measurement in neutron activation analysis of obsidian significantly better than previously obtained (about 1%). Repeated measurements on a single sample of obsidian from a deposit near Chivay, Arequipa, Peru, showed a precision (average coefficient of variation) of 0.19% for the 6 best-measured elements, the value anticipated from the known random errors of measurement. In measurement of samples made from 7 different obsidian nodules from two locations near Chivay, a group of 5 had a spread of 0.30% for the 6 elements measured with counting statistics of better than 0.3% (and 1.8% for the remaining 6 elements).