We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -a lattice-based, fractional quantum Hall state of light. [3]. On the other hand, the recent experimental realization of topological band structures in arrays of photonic modes [4,5] points to the intriguing possibility of realizing strongly-correlated interacting topological states of light [6,7]. Given that photonic systems are prepared and probed differently [8], typically have no chemical potential [9], and exhibit different decoherence mechanisms [10,11] as compared to their electronic counterparts, interacting topological states of light will open new avenues to the study of exotic physics [6]. Furthermore, such states might enable the construction of numerous robust, i.e. topologically protected, optical devices such as filters [6], switches, and delay lines [12,13]. Finally, once such highly non-classical states of light are released onto freely propagating non-interacting modes, they might be usable as resources for enhanced precision measurements and imaging [14].While strong interactions between microwave photons are readily achievable [15][16][17][18][19][20], the realization of strong high-fidelity interactions between optical photons has remained a challenge [21][22][23]. Only recently, the required strong interaction between optical photons has been implemented in a robust fashion by transforming photons into superpositions of light and highly excited atomic Rydberg states, thus forming polaritons. These polaritons inherit strong dipolar interactions from Rydberg states [24][25][26][27][28][29][30][31][32] and -together with artificial gauge fields that arise naturally in dipolar systems via the Einstein-deHaas effect [3,33,34] -constitute an ideal platform for realizing interacting topological states of light [35][36][37][38].In this Letter, we present the first example of a fractional Chern insulator of photons (or polaritons) in such a medium. The particular insulator we construct corresponds to the ν = 1/2 filling fraction of the familiar Laughlin fractional quantum Hall state, in which an ad- arXiv:1411.6624v1 [cond-mat.quant-gas]