  We propose a new inflationary scenario in type IIB Calabi-Yau
compactifications, where the inflaton is a K\"ahler modulus parameterising the
volume of an internal four-cycle. The inflaton potential is generated via
poly-instanton corrections to the superpotential which give rise to a naturally
flat direction due to their double exponential suppression. Given that the
volume mode is kept stable during inflation, all the inflaton-dependent higher
dimensional operators are suppressed. Moreover, string loop effects can be
shown to be negligible throughout all the inflationary dynamics for natural
values of the underlying parameters. The model is characterised by a reheating
temperature of the order $T_{\rm rh}\simeq 10^6$ GeV which requires $N_e \simeq
54$ e-foldings of inflation. All the inflationary observables are compatible
with current observations since the spectral index is $n_s \simeq 0.96$, while
the tensor-to-scalar ratio is $r\simeq 10^{-5}$. The volume of the Calabi-Yau
is of order $10^3$ in string units, corresponding to an inflationary scale
around $10^{15}$ GeV
