Here's another version, with the lead chip an octave lower. It took me far too long to decide which of the two to use!
The original, of course, was composed by Roland Orzabal and performed by Tears for Fears, the band that Orzabal and Curt Smith founded in the early 1980s. The slower arrangement used here is derived from a cover by Michael Andrews and Gary Jules, famously used in the film Donny Darko and a big hit in its own right.
The mix was made very simply. First, I found one of the countless MIDI arrangements of "Mad World" on the 'net (I wish I could credit someone, but they're naked of metadata) and imported it into Reason, a popular music-making app. From there, the notes and instrumentation are easy to edit; a verse was removed for length, drums added, and some of the sections edited or re-keyed to sound better with square waves. (A square wave, for the uninitiated, describes the shape of the waveform that creates the bleepy noise used in the arrangement, creating a distinctively primitive chipmusic-style sound.)