It's a rumour you often hear on Chao messageboards from the less reliable kind of person, so most people just disregard it. The truth is, there is in fact something that might be considered third evolution. It's to do with the underlying mechanics of Chao in SA2.
To recap - there are four main stats: Swim, Fly, Run and Power. Thus a Chao has four different evolutionary paths, not including Stamina.
But these four stats actually link together to affect second evolution. They effectively become two stats on a sliding scale.
Swim-------------------------Run Fly -------------------------Power
A newly evolved Dark Run Chao would have both stats smack in the middle:
Age 0 Swim------------|-------------Run Fly ------------|-------------Power
But for a fully evolved Dark Run/Run (Shadow) Chao, the scale would look like this:
Age 3 Swim-------------------------|Run (+100%) Fly ------------|-------------Power (+0%)
Second evolution is time based. You can speed it up by feeding a lot of fruit to your Chao. This makes the Chao age faster physically but remain the same in game years.
Going back to that Chao: if you never give your Dark Run Chao any more items, when he is older the Chao's stats still look like this:
Age 3 Swim-------------|-------------Run (+0%) Fly -------------|-------------Power (+0%)
Because of his age, he has reached second evolution, but it will be Dark Run/Stamina. Stamina is the default, just like in first evolution.
Third evolution happens when the Chao's stats end up looking like one of these:
Age 3 Swim-------------------------|Run (+100%) Fly -------------------------|Power (+100%)
Age 3 Swim-------------------------|Run (+100%) Fly |-------------------------Power (-100%)
Age 3 Swim|-------------------------Run (-100%) Fly -------------------------|Power (+100%)
Age 3 Swim|-------------------------Run (-100%) Fly |-------------------------Power (-100%)
These Chao can look very different from normal, and are sometimes glitched up with parts being very odd shapes or just not in the right place.
To get a third evolution Chao, just raise your Chao with a lot of Run OR Swim items, then give him a lot of Fly OR Power items.
The page on evolution cancel might interest you...