The Study Group on New Accelerators at CERN has worked out a proposal to add a pair of intersecting storage rings to the existing 28-GeV proton synchrotron. Accelerated protons injected into both rings would circulate in opposite directions and could collide in eight regions where the rings intersect. The working principle, general layout, and expected performance figures of the proposed research facility are given. The average residual gas pressure in the system must be 10−9 torr in order to have a useful lifetime of about 12 h. In the colliding beam areas even a pressure of 10−10 to 10−11 Torr is very desirable in order to keep the back-ground from residual gas scattering low enough for the observation of p-p scattering. The basic concept of the ultrahigh-vacuum system for the intersecting storage rings is described. Experimental studies on the main vacuum problems have been started.