  We obtain leading- and next-to-leading order predictions of chiral
perturbation theory for several prominent moments of nucleon structure
functions. These free-parameter free results turn out to be in overall
agreement with the available empirical information on nearly all of the
considered moments, in the region of low-momentum transfer ($Q^2 < 0.3$
GeV$^2$). Especially surprising is the situation for the spin polarizability
$\delta_{LT}$, which thus far was not reproducible in chiral perturbation
theory for proton and neutron simultaneously. This problem, known as the
"$\delta_{LT}$ puzzle," is not seen in the present calculation.
