Kamisama ni Natta hi The Day I Became a God
One day during Youta Narukami's last summer vacation of high school, a girl named Hina suddenly appears and proclaims herself "the All-Knowing God." Hina announces to the thoroughly confused Youta, "The world will end in 30 days." Youta then witnesses Hina's god-like powers of prophecy, convincing him that her powers are real. Hina's naive innocence belies her powers, and she decides to live at Youta's home for some reason. Thus begins an eventful summer before the end of the world.
[Source: Anime News Network]