We report on single-molecule fluorescence measurements performed on the phycobiliprotein allophycocyanin (APC). Our data support the presence of a unidirectional Forster-type energy transfer process involving spectrally different chromophores, alpha84 (donor) and beta84 (acceptor), as well as of energy hopping amongst beta84 chromophores. Single-molecule fluorescence spectra recorded from individual immobilized APC proteins indicate the presence of a red-emitting chromophore with emission peaking at 660 nm, which we connect with beta84, and a species with the emission peak blue shifted at 630 nm, which we attribute to alpha84. Polarization data from single APC trimers point to the presence of three consecutive red emitters, suggesting energy hopping amongst beta84 chromophores. Based on the single-molecule fluorescence spectra and assuming that emission at the ensemble level in solution comes mainly from the acceptor chromophore, we were able to resolve the individual absorption and emission spectra of the alpha84 and beta84 chromophores in APC.