  We construct explicit examples of fibre inflation models which are globally
embedded in type IIB orientifolds with chiral matter on D7-branes and full
closed string moduli stabilisation. The minimal setup involves a Calabi-Yau
threefold with h^{1,1}=4 Kaehler moduli which features multiple K3 fibrations
and a del Pezzo divisor supporting non-perturbative effects. We perform a
consistent choice of orientifold involution, brane setup and gauge fluxes which
leads to chiral matter and a moduli-dependent Fayet-Iliopoulos term. After
D-term stabilisation, the number of Kaehler moduli is effectively reduced to 3
and the internal volume reduces to the one of fibre inflation models. The
inflationary potential is generated by suitable string loop corrections in
combination with higher derivative effects. We analyse the inflationary
dynamics both in the single-field approximation and by numerically deriving the
full multi-field evolution in detail. Interestingly, we find that the Kaehler
cone conditions set strong constraints on the allowed inflaton field range.
