We introduce a simple string model of inflation, in which the inflaton field
can take trans-Planckian values while driving a period of slow-roll inflation.
This leads naturally to a realisation of large field inflation, inasmuch as the
inflationary epoch is well described by the single-field scalar potential $V =
V_0 (3-4 e^{-\hat\varphi/\sqrt{3}})$. Remarkably, for a broad class of vacua
all adjustable parameters enter only through the overall coefficient $V_0$, and
in particular do not enter into the slow-roll parameters. Consequently these
are determined purely by the number of \e-foldings, $N_e$, and so are not
independent: $\varepsilon \simeq \frac32 \eta^2$. This implies similar
relations among observables like the primordial scalar-to-tensor amplitude,
$r$, and the scalar spectral tilt, $n_s$: $r \simeq 6(n_s - 1)^2$. $N_e$ is
itself more model-dependent since it depends partly on the post-inflationary
reheat history. In a simple reheating scenario a reheating temperature of
$T_{rh}\simeq 10^{9}$ GeV gives $N_e\simeq 58$, corresponding to $n_s\simeq
0.970$ and $r\simeq 0.005$, within reach of future observations. The model is
an example of a class that arises naturally in the context of type IIB string
compactifications with large-volume moduli stabilisation, and takes advantage
of the generic existence there of Kahler moduli whose dominant appearance in
the scalar potential arises from string loop corrections to the Kahler
potential. The inflaton field is a combination of Kahler moduli of a K3-fibered
Calabi-Yau manifold. We believe there are likely to be a great number of models
in this class -- `high-fibre models' -- in which the inflaton starts off far
enough up the fibre to produce observably large primordial gravity waves.