Many years of observation have established that the solar wind flow at 1 AU normally is both supersonic and super-Alf¿nic. However, for portions of an ~5-hour period on November 22, 1979, the solar wind flow speed (~320 km s-1) observed at ISEE 3 was considerably less than the Alfv¿n speed (~540 km s-1) that resulted from an abnormally low ion density (~0.07 cm-3). The origin of this sub-Alfv¿nic flow remains uncertain: the flow was not associated in any obvious way with the rarefraction region of a high-speed stream or shock wave distubance. Intermittent observations of the flow within the earth's magnetosheath were made with instruments aboard ISEE 1 and 2 during the period when the solar wind flow was sub-Alfv¿nic. The bulk of the magnetosheath plasma was compressed, heated, and slowed relative to the upstream solar wind and was directed around the magnetosphere. Superposed on this flow was a hot, suprathermal ion beam with mean energy ~1 keV directed along the magnetic field towards the magnetosphere. These observations suggest that the bow shock neither dissipated nor disappeared when the solar wind flow was sub-Alfv¿nic.