  Using recent precise hadronic tau-decay data on the V-A spectral function and
general properties of QCD such as analyticity, the operator product expansion
and chiral perturbation theory, we get accurate values for the QCD chiral order
parameters L_10 and C_87. At order p^4 we obtain
L_10^r(M_rho)=-(5.22+-0.06)10^-3, whereas at order p^6 we get
L_10^r(M_rho)=-(4.06+-0.39)10^-3 and C_87^r(M_rho) = (4.89+-0.19)10^-3 GeV^-2.
