We provide the most accurate results for the QCD transition line so far. We optimize the definition of the crossover temperature T-c, allowing for its very precise determination, and extrapolate from imaginary chemical potential up to real mu(B) approximate to 300 MeV. The definition of T-c adopted in this work is based on the observation that the chiral susceptibility as a function of the condensate is an almost universal curve at zero and imaginary mu(B). We obtain the parameters kappa(2) = 0.0153(18) and kappa(4) = 0.00032(67) as a continuum extrapolation based on N-t = 10, 12, 16 lattices with physical quark masses. We also extrapolate the peak value of the chiral susceptibility and the width of the chiral transition along the crossover line. In fact, both of these are consistent with a constant function of mu(B). We see no sign of criticality in the explored range.