http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN
How can the oldest stars in the Universe be older than the Universe?
Of course the Universe has to be older than the oldest stars in it. So this question basically asks: which estimate is wrong -
The age of the Universe
The age of the oldest stars
Both
The age of the Universe is determined from its expansion rate: the Hubble constant, which is the ratio of the radial velocity of a distant
galaxy to its distance. The radial velocity is easy to measure, but the distances are not. THUS THERE IS CURRENTLY A 15% UNCERTAINTY IN THE HUBBLE CONSTANT.
Determining the age of the oldest stars requires a knowledge of their luminosity, which depends on their distance. This leads to a 25%
uncertainty in the ages of the oldest stars due to the difficulty in determining distances.
Thus the discrepancy between the age of the oldest things in the Universe and the age inferred from the expansion rate is within the
current margin of error. In fact, in 1997 improved distances from the HIPPARCOS satellite suggested that this discrepancy has vanished.
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