HD 140283 is an extremely metal-deficient and high-velocity subgiant in the solar neighborhood, having a location in the Hertzsprung–Russell diagram where absolute magnitude is most sensitive to stellar age. Because it is bright, nearby, unreddened, and has a well-determined chemical composition, this star avoids most of the issues involved in age determinations for globular clusters. Using the Fine Guidance Sensors on the Hubble Space Telescope, we have measured a trigonometric parallax of 17.15 ± 0.14 mas for HD 140283, with an error one-fifth of that determined by the Hipparcos mission. Employing modern theoretical isochrones, which include effects of helium diffusion, revised nuclear reaction rates, and enhanced oxygen abundance, we use the precise distance to infer an age of 14.46 ± 0.31 Gyr. The quoted error includes only the uncertainty in the parallax, and is for adopted surface oxygen and iron abundances of [O/H] = -1.67 and [Fe/H] = -2.40. Uncertainties in the stellar parameters and chemical composition, especially the oxygen content, now contribute more to the error budget for the age of HD 140283 than does its distance, increasing the total uncertainty to about ±0.8 Gyr. Within the errors, the age of HD 140283 does not conflict with the age of the Universe, 13.77 ± 0.06 Gyr, based on the microwave background and Hubble constant, but it must have formed soon after the big bang.