The transverse electrostatic mode of the collisionless long-wavelength Kelvin-Helmholtz instability is investigated by means of plasma simulation. The configuration studied involves a sheared velocity flow perpendicular in a static magnetic field. Electrostatic particle simulations permit the determination of the linear growth rates for this mode and reveal the nonlinear evolution and saturation of the instability. The linear growth rates agree with MHD results for small values of the ion gyroradius. For larger values of &rgr;i(&rgr;i/a>0.5, where a is the velocity scale length) there is a clear reduction in the growth rate. These observations are compared with the results of a two-fluid eigenvalue analysis with first order FLR corrections. The nonlinear stage of the instability is characterized by the presence of large vortices whose size is many times the initial shear length a. At saturation the simulation is dominated by the longest-wavelength mode permitted in the system. A simple model is developed to explain these results. Implications of the numerical results regarding excitation of the Kelvin-Helmholtz instability at the magnetopause boundary are discussed.