  We construct a set of chirality inducing G_4-fluxes in global F-theory
compactifications on Calabi-Yau four-folds. Special emphasis is put on models
with gauge group SU(5) x U(1)_X relevant in the context of F-theory GUT model
building, which are described in terms of a U(1)-restricted Tate model. In this
type of constructions, the G_4-flux arises in a manner completely analogous to
the U(1)_X gauge potential. We describe in detail the resolution by blow-up of
the various singularities responsible for the U(1)_X factor and the standard
SU(5) gauge group and match the result with techniques applied in the context
of toric geometry. This provides an explicit identification of the structure of
the resolved fibre over the matter curves and over the enhancement points
relevant for Yukawa couplings. The U(1)_X flux induces a chiral matter
spectrum. We compute the chiral index both of SU(5) charged matter and of SU(5)
singlets charged only under U(1)_X localised on curves which are not contained
in the SU(5) locus. We furthermore discuss global consistency conditions such
as D3-tadpole cancellation, D-term supersymmetry and Freed-Witten quantisation.
The U(1)_X gauge flux is a global extension of a class of split spectral cover
bundles. It constitutes an essential ingredient in the construction of globally
defined F-theory compactifications with chiral matter. We exemplify this in a
three-generation SU(5) x U(1)_X model whose flux satisfies all of the above
global consistency conditions. We also extend our results to chiral fluxes in
models without U(1) restriction.
