  The Buchdahl limit for static spherically symmetric isotropic stars is
generalised to the case of five dimensional Gauss-Bonnet gravity. Our result
depends on the sign of the Gauss-Bonnet coupling constant $\alpha$. When
$\alpha>0$, we find, unlike in general relativity, that the bound is dependent
on the stellar structure, in particular the central energy density. We find
that stable stellar structures can exist arbitrarily close to the event
horizon. Thus stable stars can exist with extra mass in this theory compared to
five dimensional general relativity. For $\alpha<0$ it is found that the
Buchdahl bound is more restrictive than the general relativistic case.
