He doesn't meet her in Dragon Ball Z. You probably mean Dragon Ball, in which he meets her in the episode The Ox King on Fire Mountain.
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episode 8 of Dragon Ball
They get married in episode 153 The End, The Beginning of Dragonball
Dragon Ball 134 Preliminary Peril
they get married on the last episode of dragon ball when goku has to save chi-chi's father from burning in the flaming castle episode 153
The episode in which Chi Chi and Goku fight is episode 137. It's also the episode in which Chi Chi becomes Goku's fiancee.