Refers to a scene in the movie "Spartacus" starring Kirk Douglas as Spartacus. After the army of former Roman slaves led by Spartacus is defeated in battle by legions of the Roman army, a Roman general stands before the captured surviving members of the slave army and demands that they turn over Spartacus, or else all of the former slaves will be executed. Upon hearing this and not wanting his friends to be executed, Spartacus stands up and says "I am Spartacus." However, the loyalty of his friends is so great that each of them stands forward in succession, shouting "I am Spartacus!" until the shouts dissolve into a cacophony of thousands of former slaves each insisting "I am Spartacus!" Bewildered and still not knowing which of them is Spartacus, but impressed by the loyalty he inspires in his army, the Roman general has all of the slaves crucified in a miles-long display alongside the Appian Way leading back to Rome.
Thus the phrase "I am Spartacus!" is often used to humorously start a chorus of responses of "No, I am Spartacus" among a group.
Person enters chat room and types "I am Spartacus."
100 other people in the chat room then respond with "No, I am Spartacus!", "I am Spartacus!", etc.