The Enterprise pursues aliens responsible for destroying a starbase--the lizark-like Gorn, when Kirk and the Gorn captain are both transported to the surface of a planet to resolve their differences in personal combat. The aliens responsible for transporting them, the Metrons, will destroy the loser. When Kirk wins by creating gunpowder, he requests mercy for the Gorn, impressing the Metrons, who conjecture that Humanity may one day advance beyond savagery.
Notes
Fredric Brown is credited as the author of this episode, but in fact the story was written by Gene Coon (perhaps unconsciously inspired by Brown) and the credit was given when the similarities to Brown's story were noticed. D.C. Fontana says:
According to the on-air credits, the script for "Arena" was based on the Frederic Brown short story of the same name. "What happened," says Dorothy Fontana, "is that Gene Coon wrote the story as an original. When it was read by research, they said, 'Oh, this is very much like the Frederic Brown story.' Gene said, 'Yes, you're right. I must have read it and didn't realize it.' So he instantly gave credit to Frederic Brown and Mr. Brown was properly paid. The way the development came about, the relationship between the antagonists — Kirk and the Gorn — had a lot of nice stuff to it. It could have been just a brute contest, but it wasn't. It turned out not to be that way."