  The chiral critical surface is a surface of second order phase transitions
bounding the region of first order chiral phase transitions for small quark
masses in the {m_{u,d}, m_s,\mu} parameter space. The potential critical
endpoint of the QCD (T,\mu)-phase diagram is widely expected to be part of this
surface. Since for \mu=0 with physical quark masses QCD is known to exhibit an
analytic crossover, this expectation requires the region of chiral transitions
to expand with \mu for a chiral critical endpoint to exist. Instead, on coarse
N_t=4 lattices, we find the area of chiral transitions to shrink with \mu,
which excludes a chiral critical point for QCD at moderate chemical potentials
\mu_B < 500 MeV. First results on finer N_t=6 lattices indicate a curvature of
the critical surface consistent with zero and unchanged conclusions. We also
comment on the interplay of phase diagrams between the N_f=2 and N_f=2+1
theories and its consequences for physical QCD.
