  We study the equilibrium arrangements of polarization vortices in
(PbTiO$_3$)$_n$/(SrTiO$_3$)$_n$ superlattices by means of second-principles
simulations. We find that, at low temperatures, polarization vortices organize
in a regular arrangement in which clockwise and counter-clockwise vortices
alternate positions, leading to a crystal-like structure with well defined
handedness. This chiral crystal melts at a critical temperature $T_\mathrm{M}$
into a chiral liquid, where long-range order is lost but handedness is
preserved. At even higher temperatures, $T_\mathrm{C}$, a second phase
transition occurs, at which the chiral liquid of polarization vortices loses
its handedness. Both phase transitions can be readily identified by the
adequate choices of order parameters.
