A detailed numerical study was designed and conducted to estimate the absolute age and the uncertainty in age (with confidence limits) of the oldest globular clusters in our galaxy, and hence to put a robust lower bound on the age of the universe. Estimates of the uncertainty range and distribution in the input parameters of stellar evolution codes were used to produce 1000 Monte Carte realizations of stellar isochrones, which were then used to derive ages for the 17 oldest globular clusters. A probability distribution for the mean age of these systems was derived by incorporating the observational uncertainties in the measured color-magnitude diagrams for these systems and the predicted isochrones, The dominant contribution to the width of the distribution (approximately +/-5 percent) resulted from the observational uncertainty in RR-Lyrae variable absolute magnitudes. Subdominant contributions came from the choice of the color table used to translate theoretical luminosities and temperatures to observed magnitudes and colors, as well as from theoretical uncertainties in heavy element abundances and mixing length. The one-sided 95 percent confidence limit lower bound for this distribution occurs at an age of 12.07 x 10(9) years, and the median age for the distribution is 14.56 x 10(9) years. These age limits, when compared with the Hubble age estimate, put powerful constraints on cosmology.