This paper deals with the automated composition of music. Although music within the field of AI has been studied relatively extensively, the arena in which we operate is, to the best of our knowledge, unexplored. When it concerns computer composition, a noteworthy piece of research has involved the automated generation of the chordal notes when the underlying melody is specified. The chordal notes and beats have been generated based on models of well-known composers like Bach, Beethoven, and so on. The problem we study is the converse. We assume that the system is provided with the chords of some unknown melody. Our task is to generate a melody that flows with the given chords and which is also aesthetically and musically fitting. As far as we know, there is no research that has been reported to solve this problem and in that sense, although we have merely provided “baby steps”, our work is pioneering.