A fully self-consistent theory of the electrostatic Kelvin-Helmholtz instability in finite &bgr; plasmas is presented. The instability is driven by a parallel velocity flow which is sheared transverse to the magnetic field. The important features of our analysis are as follows: Vlasov theory is used so that finite Larmor radius effects and wave-particle resonances are properly treated; the complete coupling of electrostatic and electromagnetic oscillations is considered (i.e., both the transverse and compressional magnetic fluctuations); and the ∇ B orbit modifications (i.e., both resonant and nonresonant) are treated self-consistently. The primary result is that the electrostatic Kelvin-Helmholtz instability is stable in high &bgr; plasmas. The actual value of &bgr; for stabilization depends upon the parameters. The stabilization is mainly attributed to resonant and nonresonant ∇ &Bgr; effects. These results are applied to several space plasmas (i.e., polar cusp, cometary tails, magnetopause) and estimates of the anomalous diffusion coefficient associated with this instability are presented.