Originally posted by FrothByte
The only person in the series who'd have a chance at beating Jamie in a straight up sword fight is Loras Tyrell and Brienne of Tarth. Maybe the Hound.
Jamie actually lists the Knights/Warriors who he considered his swordsmen/warrior peers* in a Storm of Swords chapter 21:
Brienne of Tarth
Robert Baratheon (in his heyday) (deceased when he made this observation)
The White Bull, Gerold Hightower (deceased when he made this observation)
Ser Arthur Dayne (deceased when he made this observation)
Greatjon Umber
Strongboar of Crakehall
The Mountain
The Hound
But, and this is what Jaime concludes in that little inner-thought of his: He could beat them all with speed and skill.
If we are to be serious, Jaime Lannister is probably the best overall 1v1 combatant (when healthy and whole) in the series.
*He specifically says "strength."