  We explore the possibility of obtaining inflation in weakly coupled heterotic
string theory, where the model dependent axions are responsible for driving
inflation. This model can be considered as a certain extrapolation of
$m^{2}\phi^{2}$-inflation, and is an attempt to explicitly realize the so
called N-flation proposal in string theory. The instanton generated potential
for the axions essentially has two parameters; a natural mass scale $M$ and the
string coupling $g_{s}$. For isotropic compactifications leading to of order
$\mathcal{O} (10^4)$ axions in the four dimensional spectrum we find that with
$(M, g_{s})\simeq(M_{GUT}, 0.5)$ the observed temperature fluctuations in the
CMB are correctly reproduced. We assume an initially random distribution for
the vevs of the axions. The spectral index, $n_{s}$, is generically more red
than for $m^{2}\phi^{2}$-inflation. The greater the vevs, the more red the
spectral index becomes. Allowing for a wide range of vevs 55 $e$-foldings from
the end of inflation, we find $0.946\lesssim n_{s} \lesssim 0.962$. The
tensor-to-scalar ratio, $r$, is more sensitive to the vevs, but typically
smaller than in $m^{2}\phi^{2}$-inflation. Furthermore, in the regime where the
leading order theory is valid, $r$ is bounded by $r < 0.10$. The spectral index
and the tensor-to-scalar ratio are correlated. For example, $n_{s}\simeq 0.951$
corresponds to $r\simeq 0.036$.
