Chao Container #1
In the Egg Snake Chamber (green zone room), the Chao Container is just in the small room to the right.
Chao Container #2
In the Egg Fish Chamber (blue zone room), launch the rocket to break open the entrance to the large room with the big weight in the middle. In this room in the nearest right corner, the Chao Container is hidden under a wooden box. Use a drill drive to break it!
Chao Container #3
You need the Mystic Melody for this one! In the red zone, there is a large room with many pillars. In the middle is the Ancient Ruins. When you use the Mystic Melody, a portal will open that will take you to a room with the Chao Container.