I've seen this phrase in several sports stories recently, and I believe it goes back several decades. The phrase can probably be broken into two parts: choke and clutch.
I know choking refers to failing in a critical situation. I'm curious how that term came about when we don't see people physically choking (or do we?) when they lose their composure or mess up. Clutch probably originated in baseball ("clutch hitter"), but the Wikipedia article links clutch to a car's transmission (timing?). I disagree and would consider this link a folk etymology. Instead, clutch is synonymous with pinch (i.e. putting pressure on something).
It seems that baseball used the terms clutch and pinch interchangeably at the start of the 20th century, but I'm not sure if they're still equivalent today. It would make sense for other sports to borrow from baseball, though no additional examples come to mind.
Can anyone shed some light on how far back this expression goes and the terms it uses?
My source is Lajoie's Official Base Ball Guide (1906), which provides some definitions on page 51.
Best Answer
Early occurrences of 'choked up' and 'choked' in baseball settings
In the context of sports, use of choke to mean "blow an easy opportunity" seems to go back to baseball in the years shortly after World War II. The Random House Historical Dictionary of American Slang (1994): has this entry as one of its definitions of choke:
The dictionary then offers an example from Bill Roeder, Jackie Robinson (1950):
In one of the vital pennant battles in St. Louis, Robinson grabbed at his throat to signify that Bill Stewart, the umpire, was "choking up." Stewart threw him out of the game.
A second early example from baseball (also cited in the Random Hose dictionary) is from Jim Brosnan, Pennant Race (1962). Here's how Brosnan describes the scene in early June 1961 at his hotel home (during baseball season) in Cincinnati a few hours after he had blown a late lead for the Reds and lost a game to the Cubs:
These examples—particularly the Jackie Robinson one—suggest that early users of the slang term choked really did equate failing under pressure with losing the ability to breathe and to function normally, and thus with failing to maintain one's composure and to perform well.
I should perhaps add that "choking up" as Jackie Robinson used the term has nothing to do with "choking up" in the sense of gripping a bat one or more inches above the knob of the bat. In the latter case, the thin part of the bat handle is imagined as the neck of the bat (the widest part of the bat is called its head), so "choking up on the bat" means gripping the bat slightly closer to the head, which, done within reason, can help improve one's bat control at the cost of some loss in power.
Early occurrence of 'choke in the clutch'
A Google Books search finds an instance of "choke in the clutch" in Paul Krassner's The Realist, issues 71–98 (1968–1974) [combined snippets]:
This article was probably published in 1968 or soon thereafter. The story appears to be a burlesque of Carlos Castañeda's The Teachings of Don Juan: A Yaqui Way of Knowledge, (which was published in 1968), and the diary entries that make up the story include dates from July and August 1968. On the other hand, the version in Google Books is presented in snippet-view format, and it appears in a collection of issues of The Realist stretching from 1968 (issue 71) to February 1974 (issue 98), so its precise publication isn't clear from the Google Books data.