A study of the linear stability of a laminar flow of an oil-water system in an inclined channel is presented. A novel shear-mode of instability, which is necessarily decaying in plane Poiseuille flow, is found to be the primary instability in certain situations. When the channel is sufficiently inclined, the long-wave mode can become unstable, regardless of the total volumetric flow rate of the fluids. The consequences to oil transport are discussed.