Faerie Conclave is the first chapter of Accel World/dural: Magisa Garden.
In a hospital, Chigira Chiaki's older brother tells Chiaki a story about a princess named Kuroyukihime, who stood at the forefront of battle. Chiaki accidentally refers to her as "Kuroyukihime" instead of "Black Lotus", and her brother gently scolds her for using that name out loud.
Some years later, Chiaki enrolls at Seibi Academy for her first day of junior high school, arriving on the second day from the United States. As an introduction, she demonstrates her strength by kicking the homeroom teacher's podium in half and announcing her intention to rule the school. She then hands the teacher an envelope containing money to fix the damages.
After school, she goes around to various martial arts clubs, including the kendo club, trying to find worthy opponents. Much to her dismay, however, no one is anywhere near robust enough to take her on. Rumors quickly spread across the school about her exploits.
Meanwhile, in the back of the school building, a girl with long hair is being bullied by three girls. Chiaki worms her way in, raring for a fight, but the girls, who have already heard of her, bust a retreat. Chiaki turns to the girl that was being bullied and says that she's got some serious guts for not even flinching when they threw a rock at her.
As she lounges in the park trying to figure out what to do, she is approached by Yuuko Hoori and Kurumi Kuruma, members of the Mathematics and Martial Arts Research Club, or "Enbuken" for short, the former wearing a bikini and a giant bear head, and the latter wearing a male noble's costume. They invite her to join their club because they're sure they can offer what she's looking for.
Chiaki follows the two upperclassmen to the clubroom, but when she enters, she finds nothing but old video games lying all over the room. She gets angry – fighting games weren't what she came her for. As she gets more and irater, Yuuko pulls a wire out of her cleavage and forcefully connects it to Chiaki's Neurolinker, engaging a Direct Wired Connection. Yuuko then attempts to send the Brain Burst program to her, but to her surprise, the file already exists on her filesystem.
Yuuko and Kurumi are immediately alarmed and mistake her for an enemy Burst Linker trying to find out their real identities. However, Chiaki repeats and again that she has no idea what they're talking about, and eventually she comes to the conclusion that her older brother must have put that program there right before he died (and she had never noticed it).
Their alarm eased, they all decide to show Chiaki the Accelerated World and enter the Normal Duel Arena. Chiaki's Duel Avatar is revealed to everyone – its name is Aluminum Valkyrie, a rare metal color with a cape and wing-like parts on her armor.