Chaiotzu, just like Tien, has two origins. In a Dragon Ball movie, he is the young, naive emperor of a distant country. However, I find it hard to believe an emperor can just vanish from his realm for decades, fighting and dying in battles and traveling the world instead of ruling. Therefore, I believe the origin of the series applies: he and Tien were students under the same sensei, who had a lasting rivalry with Roshi. So while Chaiotzu and Tien were at first enemies of Goku and Krillin, they eventually learn that their master was deceitful, and befriend Roshi and his students.

Another thing I don't quite understand about Chaiotzu is what he is exactly. He sounds and looks like an eternal child, and doesn't change in appearance at all through the decades the Dragon Ball story covers. Also, he floats way before the other Z-Senshi learn to fly, so it seems his powers are different from the others.

In Dragon Ball Z, Chaiotzu is probably the least-utilized member of the Z-Senshi. He stood by his teammates against the Saiyans, and died in a suicide attack intended to defeat Nappa (he almost did, as a matter of fact). He too received the training of King Kai, and fought the dead Ginyu Force with Yamucha and Tien. But he didn't participate in the fight againt the Androids, instead staying at Roshi's. It is here that Chaiotzu is relegated to one of the background characters, along with Oolong, Puar, and the others who just aren't powerful enough to contribute much.

Chaiotzu is probably best known for his close friendship with Tien. The two are never apart, and it is Chaiotzu's death that urges Tien to use an attack that ended up killing him. Chaiotzu seems to adore Tien in the way Gohan looks up to Piccolo, and their friendship often pairs them together both on the battlefield and off.