  We consider functions of vanishing mean oscillation on a bounded domain
$\Omega$ and prove a $\rm{VMO}$ analogue of the extension theorem of P. Jones
for $\rm{BMO}(\Omega)$. We show that if $\Omega$ satisfies the same condition
imposed by Jones (i.e.\ is a uniform domain), there is a linear extension map
from $\rm{VMO}(\Omega)$ to $\rm{VMO}(\mathbb{R}^n)$ which is bounded in the
$\rm{BMO}$ norm. Moreover, if such an extension map exists from
$\rm{VMO}(\Omega)$ to $\rm{BMO}(\mathbb{R}^n)$, then the domain is uniform.
