For several hours on March 24, 1995, the Geotail spacecraft remained near the duskside magnetotail boundary some 15RE behind the Earth while the solar wind remained very quiet (V=330 km s-1, n=14--21 cm-3) with a very steady 11-nT northward magnetic field. Geotail experienced multiple crossings of a boundary between a dense (n=19 cm-3), cool (Tp=40 eV), rapidly flowing (V=310 km s-1) magnetosheath plasma and an interior region characterized by slower tailward velocities (V=100 km s-1), lower but substantial densities (n=3 cm-3) and somewhat hotter ions (220 eV). The crossings recurred with a roughly 3-min periodicity, and all quantities were highly variable in the boundary region. The magnetic field, in fact, exhibited some of the largest fluctuations seen anywhere in space, despite the fact that the exterior magnetosheath field and the interior magnetosphere field were both very northward and nearly parallel. On the basis of an MHD simulation of this event, we argue that the multiple crossings are due to a Kelvin-Helmholtz instability at the boundary that generates vortices which move past the spacecraft. A determination of boundary normals supports Kelvin-Helmholtz theory in that the nonlinear steepening of the waves is seen on the leading edge of the waves rather than on the trailing edge, as has sometimes been seen in the past. It is concluded that the Kelvin-Helmholtz instability is an important process for transferring energy, momentum and particles to the magnetotail during times of very northward interplanetary magnetic field. ¿ 2000 American Geophysical Union