The work concerns using evolutionary methods to evolve melodic sequences, obtained through a music generative approach from Chua’s circuit, a non-linear dynamic system, universal paradigm for studying chaos. The main idea was to investigate how to turn potential aesthetical musical forms, generated by chaotic attractors, in melodic patterns, according to the western musical tradition. A single attractor was chosen from the extended gallery of the Chua’s dynamical systems. A specific codification scheme was used to map the attractor’s space of phases into the musical pitch domain. A genetic algorithm was used to search throughout all possible solutions in the space of the attractor’s parameters. Musical patterns were selected by a suitable fitness function. Experimental data show a progressive increase of the fitness values.