We report a study of the allophycocyanin trimer (APC), a light-harvesting protein complex from cyanobacteria, by room-temperature single-molecule measurements of fluorescence spectra, lifetimes, intensity trajectories, and polarization modulation. Emission spectra of individual APC trimers are found to be homogeneous on the time scale of seconds. In contrast, their emission lifetimes are found to be widely distributed because of generation of long-lived exciton traps during the course of measurements. The intensity trajectories and polarization modulation experiments indicate reversible exciton trap formation within the three quasi-independent pairs of strong interacting alpha 84 and beta 84 chromophores in APC, as well as photobleaching of individual chromophores. Comparison experiments under continuous-wave and pulsed excitation reveal a two-photon mechanism for generating exciton traps and/or photobleaching, which involves exciton-exciton annihilation. These single-molecule experiments provide new insights into the spectroscopy, exciton dynamics, and photochemistry of light-harvesting complexes.