  The renormalized next-to-leading-order (NLO) chiral low-energy constant,
$L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO)
analysis, using a combination of lattice and continuum data for the flavor $ud$
$V-A$ correlator and results from a recent chiral sum-rule analysis of the
flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The
analysis also fixes two combinations of NNLO low-energy constants, the
determination of which is crucial to the precision achieved for $L_{10}^r$.
Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with
current versions of the strange hadronic $\tau$ branching fractions as input,
we find $L_{10}^r(m_\rho )\, =\, -0.00346(32)$. This result represents the
first NNLO determination of $L_{10}^r$ having all inputs under full theoretical
and/or experimental control, and the best current precision for this quantity.
