Nonphotochemical quenching is the photoprotection mechanism by which the excess excitation energy absorbed by the light harvesting complex LHCII is dissipated through the protein scaffold as heat. Using the quenched structure of LHCII obtained from crystallographic experiments, the potential quenching of photoexcited excitons by aggregates of chlorophylls is theoretically investigated. In monomeric LHCII there is a hierarchy of length scales resulting in a hierarchy of energy scales that determine the interpigment direct Coulomb coupling. We propose a model whereby eight chlorophylls are coupled quantum mechanically into four dimers, with exciton transfer between these dimers and the remaining six single chlorophylls proceeding incoherently via Forster transfer. The chlorophyll dimer Chla604-Chlb606 possesses a quasi-parallel geometry, resulting in a weakly dipole-allowed low-lying excited state. This weakly allowed state is accessible via exciton transfer to a higher, strongly allowed state followed by fast vibrational relaxation. This parallel, H-type aggregate can potentially function as an exciton trap. Calculated Forster transfer rates between single chlorophylls and chlorophyll dimers are used in a simulation of exciton transfer in monomeric LHCII to explore this possibility. It is found that Chla604-Chlb606 has a short-lived enhanced population (on the time scale of similar to picoseconds), but not a long-time resident population. The fluorescence quantum yield of the model was calculated to be phi(F) = 0.38. Comparison of this result with phi(F) similar or equal to 0.26 for unquenched LHCII in dilute solution and phi(F) similar to 0.06 for the highly quenched LHCII crystal reveals that the proposed model does not account for the quenching observed in the LHCII crystal. We therefore conclude that the formation of chlorophyll dimers is not the main cause of excitonic NPQ in LHCII.