We consider the ground state of the quantum Ising model with transverse field $h$ in one dimension in a finite volume \[ Λ{_{m}:=\{-m,-m+1,\ldots,m+L\}\ .}% \] For $h$ sufficiently large we prove a bound for the entanglement of the interval $Λ_{0}:=\left\{ 0,..,L\right\} $ relative to its complement $Λ_{m}\backslashΛ_{0}$ which is uniform in $m$ and $L$. The bound is established by means of a suitable cluster expansion.