We describe the synthesis of a branched polyethylene-based polymer containing randomly spaced fluorescent dyes (phenanthrene or anthracene) along the polymer backbone. The dyes were introduced via ester exchange into the ethylene-methyl acrylate copolymer. Fluorescence and fluorescence-decay experiments indicated that the dyes were distributed randomly in a purely amorphous matrix. There was no indication of dye aggregation or of an enhanced local dye concentration of the sort that might be expected in a semicrystalline matrix.