  [Context]. The standard solar model fails to predict the very low lithium
abundance in the Sun, which is much lower than the proto-solar nebula. This Li
problem has been debated for decades, and it has been ascribed either to planet
formation or to secular stellar depletion. In order to test the evolution of
Li, it is important to find solar twins in a range of ages. Also, the study of
stars similar to the Sun is relevant in relation to the signature of
terrestrial planet formation around the Sun. [Methods]. We acquired
high-resolution (R=110,000), high S/N (~300) ESO/VLT UVES spectra of several
solar twin candidates and the Sun (as reflected from the asteroid Juno). Among
the solar twin candidates we identify HIP 114328 as a solar twin and perform a
differential line-by-line abundance analysis of this star relative to the Sun.
[Results]. HIP 114328 has stellar parameters Teff = 5785+/-10 K, log g =
4.38+/-0.03, [Fe/H] = -0.022+/-0.009, and a microturbulent velocity 0.05+/-0.03
km/s higher than solar. The differential analysis shows that this star is
chemically very similar to the Sun. The refractory elements seem even slightly
more depleted than in the Sun, meaning that HIP 114328 may be as likely to form
terrestrial planets as the Sun. HIP 114328 is about 2 Gyr older than the Sun,
and is thus the second oldest solar twin analyzed at high precision. It has a
Li abundance of A(Li)NLTE <= 0.46, which is about 4 times lower than in the Sun
(A(Li)NLTE = 1.07 dex), but close to the oldest solar twin known, HIP 102152.
[Conclusions]. Based on the lower abundances of refractory elements when
compared to other solar twins, HIP 114328 seems an excellent candidate to host
rocky planets. The low Li abundance of this star is consistent with its old age
and fits very well the emerging Li-age relation among solar twins of different
ages.
