A linear, electrostatic, kinetic theory of velocity-sheared inhomogeneous electron streams flowing parallel to a magnetic field is presented. Our development, which includes the effects of a density gradient, background plasma, and electron collisions, is valid for arbitrary Tes/Ti and Teb/Ti, where Tes, Teb, and Ti are the temperatures of the sheared electrons, background electrons, and background ions, respectively. For hot electron streams Tes/Ti ≫1 and Tes ≫Teb, we find a new resonant instability driven by velocity shear with frequency near the lower hybrid frequency. This mode is characterized by wave numbers k such that krLes ≲1, where rLes is the sheared electron gyroradius and is damped by collisional effects. Application is made to wave turbulence in the auroral zone and solar corona.