On a rooftop one night, a girl with a sniper rifle targets a guy who just came out of a store. She calls her target Accelerator, but when she fires, the gun explodes, and she’s thrown back with a severe arm injury. The girl who resembles Misaka Mikoto now tries to flee, but she’s cornered by the same guy she tried to shoot. Sometime later, Touma is heading home from school when he stops off to get a drink from a vending machine. He sticks a 2000 yen bill into it, and much to his dismay, the machine eats the money without giving him a drink or change. Mikoto then appears and kicks the machine to get it to spit out a drink, and she laughs when she finds out how the machine ate Touma’s money. She offers to get it back for him and uses her electric power to force the machine to spit out multiple cans, but Touma doesn’t want to be an accessory to a crime and tries to run away. Mikoto gathers up all the cans anyway and tracks him down, and Touma has no choice but to accept them. In the ensuing conversation, he learns that he had defeated her, but because he doesn’t have his memories, he has no idea in what.

Mikoto is caught off guard when Kuroko finds her sitting with Touma. Kuroko assumes that Mikoto is meeting secretly with Touma, but Mikoto angrily denies that Touma is her boyfriend. When Mikoto tries to strike Kuroko with her lightning, Kuroko teleports away. Another girl then appears, this one a spitting image of Mikoto, and she identifies herself as Mikoto’s little sister and refers to herself as simply Misaka. Frustrated, Mikoto leads Misaka away despite Misaka’s objections. Touma is left to go home by himself with all the canned drinks, and along the way, he trips on a ball. While lying on the ground, he’s approached by a Misaka and is able to identify her after catching a glimpse of her panties since he noticed earlier that Mikoto had been wearing shorts under her skirt. Misaka carrying with her a pair of military goggles and explains to Touma that, unlike her sister, she doesn’t have the skill to see electron beams and magnetic field lines, so she needs a device to visualize them.

Misaka helps Touma carry the canned drinks back home, and at the apartment building, they run into the stepsister of his classmate Tsuchimikado. Her name is Maika, and she goes to a maid school. Upstairs, the two find Index and Himegami gathered around Sphinx because the cat is covered in fleas. Index’s idea is to use a sage plant to get rid of them while Himegami wants to use what she calls a magical spray, but the ultimate solution comes from Misaka who uses her electricity to fry only the fleas. After doing this and placing the drinks on the ground, Misaka leaves. The next day while in class, Touma learns from Komoe that Mikoto is ranked third in the city and was originally a Level 1 who worked really hard to get to Level 5. When he runs into her again that afternoon, she comments on how she hates the blimp that flies around announcing the topic of the day because it means that man is following policies decided by machines.

Touma realizes that she’s talking about something called the Tree Diagram which she explains is officially a man-made weather data analysis satellite that was launched by the city. It’s supposedly the world’s most powerful super computer, but Mikoto questions if something so absurd even exists. She follows that up by hitting Touma on the head and laughing it all off before walking away. Touma barely takes another dozen steps when he runs into Misaka trying to feed a cat, and she explains that it’s impossible for her to do so because she has a fatal flaw. Her body always generates a weak magnetic field, and although humans can’t perceive it, animals can. Nevertheless, she’s afraid that the cat will be taken to the public health department because she knows how animals are treated there. Touma has no choice but to take the cat with him as he walks with Misaka, and he suggests that she give it a name. Her preferences, however, turn out to be Inu (Dog), ‘Tokugawa Ieyasu, and Schrödinger.

The two stop at a book store to check out some books on taking care of cats, and because he can’t bring the cat inside, Touma tosses it to Misaka. After she catches the cat, Touma advises her to get over the obstacle of her body generating that magnetic field. While Touma is inside, Misaka suddenly senses someone behind her, and she places the cat down before turning to face him. That person is Accelerator, and he has no trouble defeating Misaka in a fight in a back alley. As he approaches her, he questions who the strongest Level 5 in the city is.