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 using lattice QCD calculations with the highly improved staggered quarks action. 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  MeV≲m_{π}≲163  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 cutoff, corresponding to lattices with temporal extents N_{τ}=6, 8, and 12. After thermodynamic, continuum, and chiral extrapolations, we find the chiral phase transition temperature T_{c}^{0}=132_{-6}^{+3}  MeV.