The Earth is being invaded by the mysterious Oni. The Earth has one last chance to save itself. Randomly chosen by a computer to be Earth's savior, Ataru Moroboshi must defeat Invader's daughter Lum in a game of tag. Ataru has ten days in which he must grab Lum's horns or else Earth is doomed. Being the lecherous punk that Ataru is, he jumps on the chance to chase down such a pretty girl as Lum. Figuring that this challenge will be a piece of cake, Ataru rushes into the race and attempts to capture Lum. But when he finds out that she has the ability to fly, he soon realizes his dilemma.
On the night of the ninth day, Shinobu, Ataru's sort-of-girlfriend, promises to marry Ataru if he beats Lum. Convinced that he will never get a better chance for a girl, Ataru decides to do anything in order to win. On the last day of the challenge, Ataru steals Lum's bikini top, and as she chases after it, Ataru grabs her horns. Excited about Shinobu's proposal, Ataru yells out that now he can get married. Lum interprets this as a proposal to her, and she accepts.
Lum falls deeply in love with Ataru, but Ataru doesn't want to marry Lum. Shinobu gets very mad at Ataru for going with Lum, but he can't do anything about it. As another of her oni powers, Lum can deliver high-voltage electric shocks. This helps to keep Ataru in line. Between all this and the fact that Ataru is the most unlucky person in the entire universe, he stumbles upon many strange events and meets even more weird people.
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