Due to the fact that a baby chao that was made by two adult chao mating retains traits from it's parents, this opens up a door to many possibilities for making glitched, translucent, invisible, or just very cool chao in general! This is because (or at least I am assuming) Sega never planned ahead for people to start mating types of chao that just seemingly shouldn't have been mated / matched. Or just didn't plan an outcome for some types of combinations, so it was left to us to see how the chao mess up when two odd parents mate.
To continue this, the quality's that I atleast I know that are taken from the parents are the following, the newborns grades and color. Now, when we're talking about the chao taking the parents grades, it's a mix between the parents grades. Now with grades, the newborn chao can either take a whole grade from either parent, or a neutralizing round off from both of the parents. The idea of it rounding off would be, say one parent had a D, and the other chao had a B in the same particular stat, the new born would then have a C. In the idea of the newborn taking a whole grade, you'd have to say that one parent had a B, while the other parent had a C in the same particular stat. In this instance the newborn can either take a B or a C, since there is really no way to mix the both.
When the newborn chao is taking a color from the adult chao, it can take either of the parents color. Say you mated a Red Chao with a Green Chao. The newborn would then either be RED or GREEN as a main color. The advancement really picks up when the newborn chao's parents were two tone. If the parents were a Red Two Tone and a Green Monotone (one color), the newborn could be either Red monotone, Green Monotone, Red Twotone, or Green twotone. I'm sure by now you can really see how by breeding chao you may not always get what you want the first time. (That's why it's good to save your game prior to mating incase you want to restart & retry.)
What makes chao even more difficult is when the newborns parents had parents! This blows the possibilities out of proportion, and could be explained but is very difficult and not 100% confirmed if grandparent qualities are actually taken (but I'm pretty sure they are). I believe I take the grandparent assumption into place though, because when my newborns parents had parents, the grading never came out exactly right or how it was suppose too, and it sometimes had very rare cases of an seemingly impossible color UNLESS the parents had parents. So this was how my theory has came into place. So e-mail me if you know the truth. That's all on chao breeding!