We propose a new inflationary scenario in type IIB Calabi-Yau compactifications , where the inflaton is a Kähler 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 _ { 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 .