  The first discoveries of exoplanets around Sun-like stars have fueled efforts
to find ever smaller worlds evocative of Earth and other terrestrial planets in
the Solar System. While gas-giant planets appear to form preferentially around
metal-rich stars, small planets (with radii less than four Earth radii) can
form under a wide range of metallicities. This implies that small, including
Earth-size, planets may have readily formed at earlier epochs in the Universe's
history when metals were far less abundant. We report Kepler spacecraft
observations of KOI-3158, a metal-poor Sun-like star from the old population of
the Galactic thick disk, which hosts five planets with sizes between Mercury
and Venus. We used asteroseismology to directly measure a precise age of
11.2+/-1.0 Gyr for the host star, indicating that KOI-3158 formed when the
Universe was less than 20% of its current age and making it the oldest known
system of terrestrial-size planets. We thus show that Earth-size planets have
formed throughout most of the Universe's 13.8-billion-year history, providing
scope for the existence of ancient life in the Galaxy.
