Here, we explore the chemical space of all virtually possible organic molecules focusing on ring systems, which represent the cyclic cores of organic molecules obtained by removing all acyclic bonds and converting all remaining atoms to carbon. This approach circumvents the combinatorial explosion encountered when enumerating the molecules themselves. We report the chemical universe database GDB4c containing 916 130 ring systems up to four saturated or aromatic rings and maximum ring size of 14 atoms and GDB4c3D containing the corresponding 6 555 929 stereoisomers. Almost all (98.6%) of these ring systems are unknown and represent chiral 3D-shaped macrocycles containing small rings and quaternary centers reminiscent of polycyclic natural products. We envision that GDB4c can serve to select new ring systems from which to design analogs of such natural products. The database is available for download at www.gdb.unibe.ch together with interactive visualization and search tools as a resource for molecular design.