The interaction of 1,1'-diethyl-2,2'-cyanine (PIC), a non-fluorescent cationic dye known to form emissive J-aggregates in aqueous solutions, with the polyelectrolyte poly(styrenesulfonate) (PSS) is investigated by absorption and fluorescence spectroscopy. Depending on the amount of polyelectrolyte added, three regimes are identified. At a large excess of PIC, there is an equilibrium between the PIC monomer and a non-fluorescent PIC aggregate characterized by a strong absorption band centered at 565 nm. As the amount of PSS increases, we observe the growth of the PIC J-aggregate onto the PSS backbone, characterized by a sharp absorption band at 572 nm and a narrow emission at 577 nm. At a large excess of PSS, the major species consists of PIC molecules adsorbed independently along the polyelectrolyte chains.