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Bose-Einstein condensates (BECs) represent one of the very few manifestations of purely quantum effects on a macroscopic level. The vast majority of BECs achieved in the lab to date consist of bosonic atoms, which macroscopically populate the ground state once a threshold temperature has been reached. Recently, a new type of condensate was observed - the photon BEC, where light in a dye-filled cavity thermalises with dye molecules under the influence of an external driving laser, condensing to the lowest-energy mode. However, the precise relationship between the photon BEC and symmetry-breaking phenomena has not yet been investigated. Here we consider medium-induced symmetry breaking in a photon BEC and show that it can be used as a quantum sensor. The introduction of polarisable objects such as chiral molecules lifts the degeneracy between cavity modes of different polarisations. Even a tiny imbalance is imprinted on the condensate polarisation in a 'winner takes it all' effect. When used as a sensor for enantiomeric excess, the predicted sensitivity exceeds that of contemporary methods based on circular dichroism. Our results introduce a new symmetry-breaking mechanism that is independent of the external pump, and demonstrate that the photon BEC can be used for practical purposes.