Polarized fluorescence microscopy was used to investigate the organization of domains of J-aggregates formed upon adsorption of the thiacarbocyanine dye THIATS (3,3'-disulfopropyl-5,5'-dichloro-9-ethylthiacarbocyanine) onto a Langmuir film of the oppositely charged amphiphile dioctadecyldimethylammonium bromide at the air-water interface. When combined with the measurement of the spectral properties of this film at the air-water interface, it was possible to propose a model for the orientation and packing of the aggregated dye molecules in these domains. The aggregates of THIATS formed circular domains with an average diameter of approximately 35mum. Linear polarization of the excitation light beam led to fluorescence from two opposing quadrants of these circular domains. Upon rotation of the polarizer by 90degrees, the two other opposing quadrants became fluorescent whereas the fluorescence from the former fluorescent quadrants was extinguished. The orientation of the overall transition moment of these aggregates was found to be radial with relation to the large circular domains. Therefore, we proposed a model of radial growth of aggregated THIATS molecules, from a nucleation site into circular domains where the dye molecules adopt a brickstone arrangement.