  In this article we consider the linear stability of the two-dimensional flow
induced by the linear stretching of a surface in the streamwise direction. The
basic flow is a rare example of an exact analytical solution of the
Navier-Stokes equations. Using results from a large Reynolds number asymptotic
study and a highly accurate spectral numerical method we show that this flow is
linearly unstable to disturbances in the form of Tollmien-Schlichting waves.
Previous studies have shown this flow is linearly stable. However, our results
show that this is only true for G\"{o}rtler-type disturbances.
