A chaser is a drink of something that usually follows a straight shot of whiskey, gin, tequila, or some other strong liquor. The chaser may be alcoholic or non-alcoholic. A lot of men like a shot of whiskey with a chaser of beer. A chaser may be plain water or soda water or ginger ale or perhaps Coke. The original idea was that the second drink "chased" the first one and tended to soften the effect of the first strong shot.
The title of John Collier's story has nothing to do with chasing or being chased, although the young man is chasing a girl, which might cause some confusion. In the story the word "chaser" is a euphemism for poison. The first "shot" is the love potion. The chaser is a non-detectable poison with which some of the old man's customers dispose of their wives after they have gotten tired of marriage. The old man never calls his "chaser" a poison. After all, he has to be discreet if he is dealing in substances he knows will be used for murders. When Alan Austin asks the price of the love potion he is seeking:
"It is not as dear," said the old man, "as the glove-cleaner, or life-cleaner, as I sometimes call it. No. That is five thousand dollars, never a penny less. One has to be older than you are, to indulge in that sort of thing. One has to save up for it."
What the old man also call a "glove-cleaner" or "life-cleaner" is the chaser.
John Collier's black-humor story "The Chaser" was originally published in The New Yorker in December of 1940. In those days most readers would have immediately understood what a chaser was. But the term is not heard very often anymore, perhaps because combination drinks of that kind are no longer as popular. The most common drinks with chasers in those days were a shot of whiskey with a water chaser or a shot of whiskey with a small side-glass of beer as a chaser. It might have been hard to tell what was chasing what. A lot of men might be drinking beers in a saloon and occasionally call for a shot of whiskey to expedite the process of intoxication they wanted. The whiskey might be chasing the beer or vice versa.