To do this glitch you need the Battle DLC for Sonic Adventure 2

To start the Chao Key Glitch you need to go into 2P Battle Mode and change the settings to these

The number of battles setting is crucial for this glitch to work.

Now proceed to play on any of the stages for Sonic, Shadow, Tails or whoever. Whenever someone reaches 2 wins the game will ask you if you want to play again. Say no. Whatever stage you were playing on last will send you to that stage due to the Chao Key Glitch.
This is the prompt you are looking for:

Proceed to stage select, and choose one of the following stages:

Tails' Chao Key is on Mission Street

First off once you reach this section

Your going to stand on the lowest pillar

and hover back over to here

If you hovered here correctly the camera will get stuck. All you have to do now is break the Chao box there and pick up the Key very quickly before the camera gets to you. If you pick up the key in time the key will get stuck and float behind the ring counter like so:


All thats left now is to complete the stage and upon doing so sends you to the last 2P battle stage you played on:

Shadow's Chao Key is in Radical Highway

Reach this section here with the first Chao Box

Open the box so the Key is easy to pickup

Now run a little further ahead and go to where Shadow's Fire Bracelet location is:

From there you are going to spin dash off of the edge and land on the sign, make sure the camera gets stuck too.

Line yourself up with the key and run to quickly pick it up before the camera reaches you. If done correctly the key will float and all that's left is to finish the stage, WITHOUT dying.

Never leave a stage after doing the 2P battle, as doing so will cancel the glitch.

Although there may not be many listed Chao Key Glitches for now, I hope some of you guys will suggest to me locations of them. I have tried the Chao Key Glitch with Sonic on Pyramid Cave though I don't think it works on the PC version. There is still lots to do with these two characters for now.

You can also go to Treasure Hunting Stages and Shooter Stages with this glitch too. The spawn locations may be different though so be careful. Some of the mini game stages do not work and might crash or freeze the game.