Two- and three-dimensional plasma measurements made in the early morning sector of the plasma sheet with the LASL/MPI analyzers on the ISEE 1 and 2 satellites reveal that the bulk flow of plasma there is sometimes characterized by a pronounced vortical, or circulating motion. Its effect is seen as a recurrent or continuing rotation of the bulk flow vector in a plane sometimes moderately inclined with respect to the ecliptic plane. Remarkably, this rotation has a preferred sense, i.e., clockwise when viewed from above the ecliptic plane. The period for a 360 degree rotation ranges from 5 to 20 minutes and the flow can experience several complete rotations in a relatively uninterrupted sequence. On one occasion this type of behavior of the plasma continued for 9 hours. The speed of the plasma's circulating motion ranges from ~30 km/sec to ~200 km/sec. The size of the plasma vortices is estimated as several earth radii. Most of these vortices have been observed during periods of moderate geomagnetic activity. One tentative interpretation of the observations visualizes a ''vortex street'' convecting earthward along the axis of the magnetotail.