Using the Green Bank Telescope (GBT), we have obtained accurate measurements of the $^{14}$N/$^{15}$N isotopic ratio in ammonia in two nearby cold, dense molecular clouds, Barnard~1 and NGC 1333. The $^{14}$N/$^{15}$N ratio in Barnard~1, $334 pm 50$ (3$sigma$), is particularly well constrained and falls in between the local interstellar medium/proto-solar value of $sim 450$ and the terrestrial atmospheric value of 272. The NGC 1333 measurement is consistent with the Barnard~1 result, but has a larger uncertainty. We do not see evidence for the very high $^{15}$N enhancements seen in cometary CN. Sensitive observations of a larger, carefully selected sample of prestellar cores with varying temperatures and gas densities can significantly improve our understanding of the nitrogen fractionation in the local interstellar medium and its relation to the isotopic ratios measured in various solar system reservoirs.
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