Arakawa Under the bridge [TV]
Ichinomiya is the heir to a powerful conglomerate. His motto is never to be indebted to anyone, no matter how small. However, one day, his life is saved by a strange girl living under a bridge who claims to be an alien. In order to repay the debt of his life, Ichinomiya moves in with her under the bridge.
~Thanks to cranston for the description.