In this paper we consider a model for gravity in four-dimensional space-time originally proposed by Chamseddine, which may be derived by dimensional reduction and truncation from a five-dimensional Chern–Simons theory. Its topological origin makes it an interesting candidate for an easier quantization, e.g., in the loop quantization framework. The present paper is dedicated to a classical analysis of the model’s properties. Cosmological solutions as well as wave solutions are found and compared with the corresponding solutions of Einstein’s general relativity with cosmological constant.