It could have been Jaime. It could have been Bran. It could have been Jon Snow or Daenerys Targaryen or any number of characters on Game of Thrones. There have been prophecies and theories and years of evidence pointing toward a half-dozen characters who could kill the Night King.
But, at the end of Game of Thrones Season Eight Episode Three, it was Arya Stark who killed the Night King, by jumping out of nowhere and plunging Littlefinger's dagger into his chest.
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It seemed like the battle was lost for the Army of the Living. Theon died defending Bran. Same with Jorah Mormont and sweet little Lyanna Mormont.
Then, as the Night King approached Bran, Arya jumped out of nowhere to kill him, but he spun and caught her by the throat. Before he could crush her throat, she used the move that fans have noted she once used on Brienne of Tarth.
Arya dropped her dagger to her other hand and plunged it into his body. Now, if you'll remember, that particular knife has a lot of history. It was the knife once used to attempt an assassination of Bran Stark. It has had a long path to get back to Arya Stark. In Season Seven, Littlefinger gave the dagger to Bran Stark, who then gave it to Arya (in hindsight, probably because he knew she'd kill the Night King with it).

But, it makes for a satisfying conclusion to Arya's character arc—her years of training have all come to this. It's also a satisfying conclusion to what is an immensely impressive 90-minutes of television, with a tense battle all leading up to the moment where Arya saves the day. It's also worth noting what Melisandre asked Arya right before her big moment: "What do we say to the god of death?"
Not today.
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