  We propose a natural scenario for the cosmological inflation with the
non-minimal coupling term invoking compact hyperbolic extra dimensions. Thanks
to the unique mathematical properties of compact hyperbolic space, the large
volume of extra dimensions, which provides a natural understanding of the
proper size of couplings, does not necessarily accompany with the low
Kaluza-Klein scale so that the model allows a single field inflation with a
scale around $10^{13}$ GeV. The model fulfills all the observed data and
predicts a sizable gravitational perturbation, r~0.003.
