By far the best fictional chess player on TV was the main character on "Endgame," a mystery series from Canada that aired one season on Hulu. I can't remember the (fictional) Grandmaster's name from the show, but he had been staying in a luxury hotel for a tournament when he saw his girlfriend killed by a car bomb meant for him.
He developed a severe case of agoraphobia and refused to leave the hotel OR to pay for his suite. But the hotel kept him on because he kept using his genius, week after week, to solve some mystery the hotel needed solved. He "employed" a chess master to go outside and do his legwork in exchange for playing instructive games with the GM.
It was great fun, but it was only one season, and I wish they'd bring it back.
Who would we say is the best?
Sheldon Cooper plays numerous times on BBT. Whips Leonard a lot. Of course Leonard got beat by a "Bobby Fischer" like Penny. Sheldon has eidetic memory and would likely have a prodigeous ability.
Mike Ross from Suits also has eidetic memory, they haven't shown him playing Chess but he's good at poker. Knows the odds to the decimal.
Gregory House was great at Chess. Played a game well with a prodigy in the episode "The Jerk" just to cause a symptom and find the clue to the sickness.
Sherlock Holmes and Moriarty played a notable game in a Game of Shadows.
Patrick Jane on The Mentalist played without a board and beat a good player while solving a crime involving the guy he was playing.
Kirk and Spock played 3D chess, I imagine Data from NG would be awesome as a many centuries from now android.
So many more choices I can't yet think of.
I wonder if they played a tournament what the result would be.