  The symmetry-resolved R\'enyi entanglement entropy is the R\'enyi
entanglement entropy of each symmetry sector of a density matrix $\rho$. This
experimentally relevant quantity is known to have rich theoretical connections
to conformal field theory (CFT). For a family of critical free-fermion chains,
we present a rigorous lattice-based derivation of its scaling properties using
the theory of Toeplitz determinants. We consider a class of critical quantum
chains with a microscopic U(1) symmetry; each chain has a low energy
description given by $N$ massless Dirac fermions. For the density matrix,
$\rho_A$, of subsystems of $L$ neighbouring sites we calculate the leading
terms in the large $L$ asymptotic expansion of the symmetry-resolved R\'enyi
entanglement entropies. This follows from a large $L$ expansion of the charged
moments of $\rho_A$; we derive $tr(e^{i \alpha Q_A} \rho_A^n) = a e^{i \alpha
\langle Q_A\rangle} (\sigma L)^{-x}(1+O(L^{-\mu}))$, where $a, x$ and $\mu$ are
universal and $\sigma$ depends only on the $N$ Fermi momenta. We show that the
exponent $x$ corresponds to the expectation from CFT analysis. The error term
$O(L^{-\mu})$ is consistent with but weaker than the field theory prediction
$O(L^{-2\mu})$. However, using further results and conjectures for the relevant
Toeplitz determinant, we find excellent agreement with the expansion over CFT
operators.
