Energy transfer is studied in a system consisting of Langmuir-Blodgett monolayers of the hemicyanine dye, N-(3-sulfopropyl)-4-(p-dioctylaminostyryl)pyridinium. Deposition from CHCl3 solution onto the air-water interface results in self-assembly into two-dimensional aggregates with an absorption band significantly blue-shifted (9000 cm-1) from that of the monomer in solution. Calculation of structural parameters consistent with this extremely large blue-shift, in the extended dipole approximation, indicates the structure of the aggregate is considerably more compact than the average structure observed in the PI-A isotherm. However, the residual monomer, which is <0.5% of the total population from absorption measurements, dominates the fluorescence spectrum, typically yielding excitation bands of comparable intensity to the aggregate. This observation along with the identical nature of the fluorescence emission excited in either the aggregate or monomer absorption bands leads us to propose that energy migration in this system occurs primarily from the aggregate to the monomer. Thus, the donor (aggregate) and acceptor (monomer) species differ solely in aggregation state, not in chemical structure, as in more traditional energy-transfer experiments. This study has direct implications for the possible migration pathways in a variety of systems where energy transfer is of importance.