The Chocobo Theme is the leitmotif of the series’s mascot chocobo, a usually yellow bird often usable as a steed. Each game uses a different mix of the central melody arranged in a particular style of music. It was composed by Nobuo Uematsu for Final Fantasy II, the game where chocobos debuted.
I will record this soon on my video channel for classical guitar, in the mean time you can find the MIDI render on Soundcloud.