  We present a lattice QCD based determination of the chiral phase transition
temperature in QCD with two degenerate, massless quarks and a physical strange
quark mass. We propose and calculate two novel estimators for the chiral
transition temperature for several values of the light quark masses,
corresponding to Goldstone pion masses in the range of $58~{\rm MeV}\lesssim
m_\pi\lesssim 163~{\rm MeV}$. The chiral phase transition temperature is
determined by extrapolating to vanishing pion mass using universal scaling
analysis. Finite volume effects are controlled by extrapolating to the
thermodynamic limit using spatial lattice extents in the range of $2.8$-$4.5$
times the inverse of the pion mass. Continuum extrapolations are carried out by
using three different values of the lattice cut-off, corresponding to lattices
with temporal extent $N_\tau=6,\ 8$ and $12$. After thermodynamic, continuum
and chiral extrapolations we find the chiral phase transition temperature
$T_c^0=132^{+3}_{-6}$ MeV.
