Episode Zero, also known as Trailer marketing in Japan, is a preview chapter for Vigilante - My Hero Academia: Illegals.
At U.A. High School, Izuku Midoriya wonders what a "Vigilante" is. All Might arrives to explain everything. All Might explains that a Vigilante is a person who voluntarily acts and carries out public operations in the name of public safety without regard to the law. All Might elaborates that the origin of Heroes is traced back to Vigilantes. Izuku begins understanding that at the time of the Quirk phenomenon, the entity regulating the organization of Pro Heroes did not exist; in other words, all of the first Pro Heroes were actually Vigilantes. Shota Aizawa explains that according to the current Hero Regulations, privately doling out punishment without credentials is a crime and says that in modern times, Villains and Vigilantes are considered to be the same. However, Shota states that Vigilantes are nothing more than fossils of a bygone era and the majority of Vigilantes have all but vanished.
In an alley, a criminal prepares to attack an innocent girl, demanding her to hand over her bag, threatening her with his blade arm. Suddenly, a muscular bandage-masked man appears from the air and kicks the criminal. As the criminal gets up, the muscular man grabs the criminal's blade arm, preventing him from using it and punches the criminal in the face. With the criminal knocked out, the muscular man is angry at the criminal for his evil intentions and no matter how petty the crime, they are all villains to him and he will punish every one of them. The muscular bandage-masked man is known as Knuckleduster.
Elsewhere, a female teenager is using her Quirk to fly, and is annoyed that the Hero Regulations forbid the public display of Quirks which forces her to walk on the ground like everyone else, finding the rule to be infantile. The female teenager is called Pop☆Step. She flies to the roof of a building, lands and sits on it. She is not interested in the law or rules.
In another place, a male teenager wearing a jacket with a hood similar in appearance to All Might, prepares to use his Quirk for the greater good. The male teenager uses his Quirk to sprint on the ground; he uses the speed to help find a lost cellphone and returns it to its owner, then to help guide a person around town, save a lost child and help old ladies cross the street. After completing these petty Heroics, the male teenager called Nice Guy feels wonderful.
At U.A., Shota tells Class 1-A that the Vigilantes just shown are heinous criminals and does not want them imitating them, much to Nice Guy's shock who wants to know what he did wrong. As Shota points out that he used his Quirk in a public area, All Might comments on Nice Guy's attire, wondering if he is wearing the "Official Online-Exclusive Limited Edition All Might Parka"; Nice Guy is shocked at seeing the real All Might. Shota scolds Nice Guy for not wearing a proper Hero Costume and that unqualified individuals such as him should not be gallivanting around wearing misleading clothes and performing misleading deeds. Nice Guy defends his actions in the name of helping people.
Suddenly, Knuckleduster appears and scolds Nice Guy for his criminal-like behavior while Pop☆Step comments on Nice Guy's stupidity. Shota starts calling the Police Force to arrest them, causing the Vigilantes to flee. Shota reveals that he did not actually call the police and was joking about it; Izuku wonders if it is alright not to chase after them. Shota states that guiding the lifestyles of the general populace is not a Hero's job and as long as they do not start abusing their Quirks for evil acts, they can let the Vigilantes be. Looking at it from another perspective, Shota states that simple fan admiration could lead to people becoming Vigilantes, like Nice Guy, and Heroes should keep their interactions with fans to a reasonable level, causing All Might to comment on Shota's scariness. Shota tells Class 1-A not to associate with Vigilantes, to which they reply they will not.
He continues and says that on the inside, Vigilantes are Heroes, but objectively speaking they are villains. Whatever they do, they must not imitate the actions of these "illegal heroes"!