By measuring the fluorescence photon statistics of single chains of a conjugated polymer, we determine the lifetime of the metastable dark state, the triplet exciton. The single molecule emits single photons one at a time, giving rise to photon antibunching. These photons appear bunched in time over longer time scales because of excursions to the triplet dark state. Remarkably, this triplet intermittency in the fluorescence is spontaneously suppressed over time scales of seconds, implying that either triplet formation is inhibited or that triplets are selectively quenched without the singlet fluorescence being affected. Such discrete switching in the strength of photon bunching is only seen in highly ordered and rigid chains of a ladder-type conjugated polymer. It does not occur in single dye molecules. We propose that trapped photogenerated charges on the chain selectively quench triplets but not singlets, presumably because the effective diffusion length of triplets is longer along the highly rigid ladder-type backbone.