  We compute the coefficient function for the charge-averaged W^(+/-)-exchange
structure function F_3 in deep-inelastic scattering (DIS) to the third order in
massless perturbative QCD. Our new three-loop contribution to this quantity
forms, at not too small values of the Bjorken variable x, the dominant part of
the next-to-next-to-next-to-leading order corrections. It thus facilitates
improved determinations of the strong coupling alpha_s and of 1/Q^2 power
corrections from scaling violations measured in neutrino-nucleon DIS. The
expansion of F_3 in powers of alpha_s is stable at all values of x relevant to
measurements at high scales Q^2. At small x the third-order coefficient
function is dominated by diagrams with the colour structure d_abc d^abc not
present at lower orders. At large x the coefficient function for F_3 is
identical to that of F_1 up to terms vanishing for x to 1.
