During Big Bang nucleosynthesis (BBN) in the first 15 minutes of the Universe, some 7Li was created along with isotopes of H and He. The determination of that primordial value of Li can help constrain the conditions at that time. The oldest stars with known ages can be found in globular clusters which have well-determined ages through stellar evolution models. High-resolution spectra of Li have been obtained with the Keck I Telescope and HIRES in several unevolved stars in the clusters M13 and M71 with V magnitudes of 17.6–17.9. Abundances of Li have been determined with spectrum synthesis techniques and show a range of a factor of 4. We attribute that spread to differences in initial angular momentum resulting in different amounts of spin-down, related mixing, and destruction of Li. Our results are compared with similar results for main-sequence and turnoff stars in other globular clusters. The range in age of these clusters is 11.2–14.2 Gyr for an age span of 3 Gyr. These clusters range in [Fe/H] from −0.75 to −2.24 corresponding to a factor of 30 in metallicity. The maximum in the Li abundance for these unevolved stars in all eight clusters is the same corresponding to Li/H = 3.16 × 10−10, while the predicted Li abundance, based on the deuterium abundance and the BBN predictions, is 5.24 × 10−10.