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Chi-Chi is first introduced in Dragon Ball and, of course, was trying to kill Gokou. Well, I'm not too sure what happens and I don't want to tell you lies, so somehow, she and Gokou fell in love and got married right after the Piccolo saga . A few years later, in Dragon Ball Z, she and Gokou had a 5 or 4-1/2 year old son, Gohan.
She wanted Gohan to be a scholar when he grew up so she made him study constantly. She wouldn't allow Gohan to live a lifestyle like Gokou's. But when Goten came along, she pretty much gave up on him.
She's generally a nice person, she means well for her family, but most of the time, we don't see her in a nice mood. While she doesn't have any powers (flying, ki blasts, etc.) she is rather strong compared to the regular humans we see getting blown up. There's not really much to say about her.