Topological phases in frustrated quantum spin systems have fascinated researchers for decades. One of the earliest proposals for such a phase was the chiral spin liquid, a bosonic analogue of the fractional quantum Hall effect, put forward by Kalmeyer and Laughlin in 1987. Elusive for many years, recent times have finally seen this phase realized in various models, which, however, remain somewhat artificial. Here we take an important step towards the goal of finding a chiral spin liquid in nature by examining a physically motivated model for a Mott insulator on the Kagome lattice with broken time-reversal symmetry. We discuss the emergent phase from a network model perspective and present an unambiguous numerical identification and characterization of its universal topological properties, including ground-state degeneracy, edge physics and anyonic bulk excitations, by using a variety of powerful numerical probes, including the entanglement spectrum and modular transformations.