Whether at a sports match or in a serious life situation, sometimes the front runner chokes and loses to his or her opponent. Since no one is literally choking, the word must be part of a longer idiom. And so it is.
In medieval England, when an individual was accused of a crime, he or she was given a piece of cheese and consecrated bread to eat to prove guilt or innocence. If the individual was guilty, he would choke on the bread when the Angel Gabriel came down from Heaven to stop his or her throat. Surely an innocent man (or woman) would be the winner and not choke when put to the test!
Thus the oath many would utter was, “May I choke if this is not true.” Over the years, only the word choke remains of the idiom.