Using observations from the Advanced Composition Explorer (ACE) magnetic field and plasma experiments, we investigate the magnetic, thermal, and dynamic pressure balance in the border of a high-speed stream (HSS) and an average-speed interplanetary coronal mass ejection (ICME) observed on 21--22 October (1999). We believe that the HSS compressed the ICME and intensified its internal southward magnetic field, resulting in a very intense geomagnetic storm, with peak Dst of -237 nT. In solar cycle 23 this was the only event, out of 18 very intense geomagnetic storms, i.e., peak Dst < -200 nT, which was caused by such a mechanism. We also address the solar origin of this very intense geomagnetic storm, using combined solar data from three different sources: a ground-based source, coronal hole maps from the National Solar Observatory (NSO) at Kitt Peak, and two satellite-based sources, eruption activity from the Extreme Ultraviolet Imaging Telescope (EIT) and coronal mass ejection observations from the Large Angle and Spectrometric Coronagraph (LASCO), both aboard the Solar and Heliospheric Observatory (SOHO). A coronal hole is evident just beside (to the east of) the active region from which an average-speed coronal mass ejection lifted off on 17--18 October (1999). This was the only possible solar origin of the 21--22 October interplanetary geomagnetic event.