  We present new stable solutions of the Tolman Oppenheimer Volkoff equations
for quark stars using a quark matter equation of state based on the SU(3)
Quark-Meson model that exhibits the onset of the chiral phase transition. These
new solutions appear as two stable branches in the mass-radius relation
allowing for so called twin stars, i.e. two stable quark star solutions with
the same mass, but distinctly different radii. We find solutions which are
compatible with causality, the stability conditions of dense matter, the
astrophysical constraints of the rotation of the millisecond pulsar PSR
J1748-2446ad and the 2$M_{\odot}$ pulsar mass constraint.
