  The most accurate ages for the oldest stars are those obtained for nearby
halo subgiants, because they depend almost entirely on just the measured
parallaxes and absolute oxygen abundances. In this study, we have used the Fine
Guidance Sensors on the Hubble Space Telescope to determine trigonometric
parallaxes, with precisions of 2.1% or better, for the Population II subgiants
HD 84937, HD 132475, and HD 140283. High quality spectra have been used to
derive their surface abundances of O, Fe, Mg, Si, and Ca, which are assumed to
be 0.1-0.15 dex less than their initial abundances due to the effects of
diffusion. Comparisons of isochrones with the three subgiants on the
$(\log\,T_{\rm eff}, M_V)$-diagram yielded ages of $12.08 \pm 0.14, 12.56 \pm
0.46$, and $14.27 \pm 0.38$ Gyr for HD 84937, HD 132475, and HD 140283, in
turn, where each error bar includes only the parallax uncertainty. The total
uncertainty is estimated to be $\sim\pm 0.8$ Gyr (larger in the case of the
near-turnoff star HD 84937). Although the age of HD 140283 is greater than the
age of the universe as inferred from the cosmic microwave background by $\sim$
0.4-0.5 Gyr, this discrepancy is at a level of $< 1\,\sigma$. Nevertheless, the
first Population II stars apparently formed very soon after the Big Bang.
(Stellar models that neglect diffusive processes seem to be ruled out as they
would predict that HD 140283 is $\sim 1.5$ Gyr older than the universe.) The
halo field subgiants appear to be older than globular clusters of similar
metallicities: if distances close to those implied by the RR Lyrae standard
candle are assumed, M92 and M5 are younger than HD 140283 and HD 132475 by
$\sim 1.5$ and $\sim 1.0$ Gyr, respectively.
