I'm Lum-chan the Notorious! - It's Raining Oil All Over Town

Ataru Moroboshi, an unlovely flirtatious boy, has been chosen to fight an invading alien force's champion in a 10-day game of tag. If he loses the aliens will invade Earth, but if he wins, the aliens will go home. Ataru isn't at all willing to play tag until he sees the alien's champion: the beautiful Lum. A group of admirers of Lum try to summon her UFO back to Earth, using Ataru as bait, but instead they get an intergalactic taxi that takes them though subspace, and the fare for the taxi is the value of all the oil on the planet.