Chaos Drives are parts of the G.U.N. (Guardian Units of Nations) robots found throughout the levels. By destroying those robots, you can collect the Chaos Drives within. You can then take your collected Chaos Drives into Chao World, and give them to your Chao to boost their stats.
Chaos Drives have four different colours that represent the four stats that they increase: Swim, Fly, Run, and Power. There are no Chaos Drives specifically for raising Stamina, Luck, or Intelligence. The colour of the drive you receive when you defeat a G.U.N. robot is random, so you just have to hope you get the colour you want.
Chaos Drives are good because when you give them to your Chao, it does not affect their appearance (as there are no animal parts), and it also does not decrease any stats like some animals do. On the other hand, Chaos Drives only increase one stat at a time (depending on their colour), and do not always increase that stat as much as some animals can.
Chaos Drives increase the stat's bar by 24%. This means that four Chaos Drives will almost, but not quite, level up a stat. In order to level up a stat which has an empty bar, you will need to give the Chao five Chaos Drives of the appropriate colour.
The best way to get lots of Chaos Drives quickly for your Chao is by using Tails or Eggman to collect them. You can simply start a level, destroy ten G.U.N. robots, collect their Chaos Drives, and then exit the level. Then go to a Chao Garden and your collected Chaos Drives will be scattered around the entrance for you to use.