Chaos Drives are crystallized Chaos Energy that are usually contained in devices. They seem to be power source for robots. The Chaos Drives were initially designed by Professor Gerald as a means of transferring energy to living tissue, part of his work on Project Shadow.
Chaos Drives first appear in Sonic Adventure 2 as power source for GUN Robots much like animals used for Eggman's robots. Collected and used with Chao at Chao Gardens to enhance a Chao specific skills:
With the right combination of animals, color of Chaos Drives and depending on who is raising the specific Chao can alter the outcome of the Chao to appear similar to a character.
They appear once again along with Light Cores which replenish a bit of energy to the Action Gauge while Chaos Drives restore the most. Incidentally Chaos Drives also appear as a Power Up on item boxes. Once the item box is busted it will fully restore the Action Gauge. Unlike Sonic Adventure 2 where Chaos Drives slowly fall to the ground and you pick them up, Light Cores and Chaos Drives home into you the moment the robots are destroyed. They are not used for Chao raising, as Chao gardens are not in this game.
Instead of drives, yellow "♦" shaped crystals known as Chaos Orbs can be found from defeated enemies. When collected, they increase "Experiance" and can be used on the Status Screen to increase parameters. Once parameters level up new skills can be learned.