Much of the richness in nature emerges because simple constituents form an endless variety of ordered states(1). Whereas many such states are fully characterized by symmetries(2), interacting quantum systems can exhibit topological order and are instead characterized by intricate patterns of entanglement(3,4). A paradigmatic example of topological order is the Laughlin state(5), which minimizes the interaction energy of charged particles in a magnetic field and underlies the fractional quantum Hall effect(6). Efforts have been made to enhance our understanding of topological order by forming Laughlin states in synthetic systems of ultracold atoms(7,8) or photons(9-11). Nonetheless, electron gases remain the only systems in which such topological states have been definitively observed(6,12-14). Here we create Laughlin-ordered photon pairs using a gas of strongly interacting, lowest-Landau-level polaritons as a photon collider. Initially uncorrelated photons enter a cavity and hybridize with atomic Rydberg excitations to form polaritons(15-17), quasiparticles that here behave like electrons in the lowest Landau level owing to a synthetic magnetic field created by Floquet engineering(18) a twisted cavity(11,19) and by Rydberg-mediated interactions between them(16,17,20,21). Polariton pairs collide and self-organize to avoid each other while conserving angular momentum. Our finite-lifetime polaritons only weakly prefer such organization. Therefore, we harness the unique tunability of Floquet polaritons to distil high-fidelity Laughlin states of photons outside the cavity. Particle-resolved measurements show that these photons avoid each other and exhibit angular momentum correlations, the hallmarks of Laughlin physics. This work provides broad prospects for the study of topological quantum light(22).