Aside from the Sonic, Shadow and True NiGHTS Chao, which are just regular evolutions, there are three official character Chao. These, like Chaos Chao, are immortal and do not breed. The bad news is that they cannot be acquired in the regular game.
This Chao is the only one of the three that is available outside of Japan, although getting him is very expensive. To get the Tails Chao legitimately, you need to have access to:
The Tails Chao can be acquired once per character in PSO, for each of the difficulties. To get him, you must complete the Fake in Yellow offline quest, and then go back down to Ragol before visiting the guild counter. In the final room of Forest 1, there will be three Rappies sitting and looking towards a certain area. Walk to this area and a Chao will appear.
When the Chao has finished talking, pipe back up to Pioneer Two. Outside the Guild you will see a new machine, similar to the Chao transfer devices in SA2B. Stand on the machine, connect the GBA without a game in, and turn it on. The Tails Chao will be transferred to your GBA in a temporary Tiny Chao Garden. All you have to do then is turn on SA2B and transfer him into the Gamecube Chao Garden!

When acquired legitimately, Tails Chao comes with all A ranks and a hundred points on every stat.
The other way to get a Tails Chao is to invest in an Action Replay/Gameshark device for either Game Boy Advance or Gamecube. Some Gamecube AR devices even allow you to connect your Cube to the PC and download save data off the Internet.
TAILS CHAO AR CODES:
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Changes first Chao in garden. DO NOT USE on eggs.
(SA2B) US: Carry Chao out of the garden then back in while code is on
HQ1G-0TA8-TKE57
UUH7-P89F-K2602
GEYW-WF0N-UTYBQ
(SA2B) PAL: Change is automatic
T4A7-U206-14MJ2
5XUT-6PW3-NARKX
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The Amy Chao was only available at a certain event in Japan. It is not possible to get this Chao legitimately now.

AMY CHAO AR CODES:
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Changes first Chao in garden. DO NOT USE on eggs.
(SA2B) US: Carry Chao out of the garden then back in while code is on
JHCA-GC3M-VKZTR
UUH7-P89F-K2602
D9B4-H1NR-WWK4K
(SA2B) PAL: Change is automatic
RT9F-HHC7-NMH64
BVFP-R2K8-BWQK3
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The Knuckles Chao was only available at a certain event in Japan. It is not possible to get this Chao legitimately now.
KNUCKLES CHAO AR CODES:
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Changes first Chao in garden. DO NOT USE on eggs.
(SA2B) US: Carry Chao out of the garden then back in while code is on
MN2A-GD16-A8KMP
UUH7-P89F-K2602
PZR0-8Z4H-41CX1
(SA2B) PAL: Change is automatic
NBMA-B1HA-5BHCN
C3N7-U1HG-N0XQ0
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NB: If you don't know which Chao is in the first slot in the garden, either go to a Race/Karate, or step on the transporter. The order in which Chao appear in the menu is the order of the game data.
It is highly advisable, when using AR for any game, to keep the game save backed up elsewhere. Edit your Chao on a clean card and transfer them across when everything's working.