The Amiga has been doing this from the very beginning and it's still done today, If you use the Octamed synth waveform editor you are using the Amiga as a wavetable synth, indeed this appears the term chiptune probably came from the use of this feature.
Chiptunes predate Octamed or trackers. Obviously there are several different ways to produce the effect, but easily the most common is to use very short looping samples.
Here's a 350MB collection of chip music, using wide range of different trackers:
rsync -avP zakalwe.fi::chip /local/path