A few years before the beginning of the story, certain girls and women all over the world began to manifest a power known as "Dreams of Alice," with which they can make select elements of their imaginations come true. The world powers are split into two factions: those who wish to keep these girls a secret and experiment on them, and those who wish to reveal their existence to the public and integrate them into society.
One such girl, who's been nicknamed "The Red Queen" due to her incredibly powerful Dream of Alice, escapes from the research facility holding her and sets out to explore the outside world. Eventually, she winds up meeting a florist named Zouroku: a strict old man whose catchphrase is, "I hate crooked dealings!"