In an early example, Harry F. Olson at Bell Labs used Markov chains in the 1950s to analyse the music of American composer Stephen Foster, and generate scores based on the analyses of 11 of Foster's songs.
Lejaren Hiller used a computer at Princeton in 1955 to generate the Illiac Suite (the first genuine case of music GC, according to Geraint Wiggins). Combined Markov chaining and application of rules of 16th century counterpoint. There are many good websites on this including
http://www.music.psu.edu/Faculty%20Pages/Ballora/INART55/illiac_suite.html and http://www.lim.dico.unimi.it/eventi/ctama/baggi.htm
Lejaren Hiller and Robert Baker also worked with Markov processes to produce their `Computer Cantata' in 1963.