Olympic gels are an elusive form of soft matter, comprising a 3D network of mechanically interlocked cyclic molecules. In the absence of defined network junctions, the high conformational freedom of the molecules was previously theorized to confer unique mechanical properties to Olympic gels, such as non-linear elasticity and unconventional swelling characteristics. However, the synthesis of an Olympic gel exhibiting these intriguing features is challenging, since unintended crosslinking and polymerization processes are often favored over cyclization. Here, we report the successful assembly of a true Olympic gel from a library of DNA rings comprising more than 16 000 distinct molecules. Each of these rings contains a unique sequence domain that can be enzymatically activated to produce reactive termini that favor intramolecular cyclization. We characterized the genetic, mechanical, and structural characteristics of the material by next-generation sequencing, oscillatory rheology, large-scale computational simulations, atomic force microscopy, and cryogenic electron microscopy. Our results confirm the formation of a stable Olympic gel, which exhibits unique swelling behavior and an elastic response that is exclusively determined by entanglements, yet persists on long time scales. By combining concepts from polymer physics, synthetic biology, and DNA nanotechnology, this new material class provides a flexible experimental platform for future studies into the effects of network topology on macroscopic material properties and its function as a carrier of genetic information in biological and biomimetic systems. This work moreover demonstrates that exotic material properties can emerge in systems with a high compositional complexity that is more reminiscent of biological than synthetic matter.