Secret Chao Eggs
As you know, you can find Chao eggs in the various gardens which are white, with blue spots and a yellow cap. However, there are some rare Chao eggs located in the different adventure fields for you to find, and take back to the Chao Garden!
The Gold Chao Egg - Station Square
Go to the area in Station Square where Sonic first fought Chaos 0. There is an Antique Shop nearby. If you look through the window, you can see a shiny stone on display on a pedestal. This is the Gold Chao Egg! However, every time you try to pick it up, the shops alarms go off and lock you inside! What you have to do is leave the store, and in the area outside the town hall there is an egg-shaped rock hiding in the grass. Simply take this back to the Antique Store and replace it with the Gold Egg! Now you can carry the egg back to the Chao garden.
The Silver Chao Egg - Mystic Ruins
Go to the small lake opposite Tails' house in the Mystic Ruins (where you fought Chaos 4) and run to the right-hand side of the water level. There's a little platform here that moves into the cliff if you push it. This will cause the Silver Egg to be pushed out of the side of the cliff to land safely into the water below. Now all you have to do is wait for it to float to the shore of the lake for you to pick it up and take it to the Chao garden.
The Black Chao Egg - Egg Carrier
Inside the Egg Carrier, head to the prison cells where Amy was being held captive during her adventure. If playing as Amy, go into the main section of the Egg Carrier and go to where you play the mallet game (the door next to the Hot Shelter). Walk through here and it will take you to the prison cell area. Jump on the button ouside the cell to open the door to allow you to collect the egg! Although the egg is black, the Chao inside is Grey!
For more information on the Grey vs Black Chao, please take a look at the page about Chaclon!