I believe that this question is asking for a bit of explanation as to how the title of this great short story applies to the events being narrated. I'm actually always pleased to find out that most of my students are ignorant of what a chaser beverage actually is. A lot of strong liquors don't necessarily taste all that great, so after taking a shot of something particularly strong and foul tasting, it is common to follow up with something that washes the taste away. The second drink "chases" the first drink. Beer is often a common chaser, but the first drink and/or the chaser don't have to be alcoholic. I use the chaser concept with my elementary aged children when they have to drink a little "shot" of cough medicine. They usually chase it down with milk or apple juice.
The drink-chaser concept applies to this story because the salesman is quite confident that Alan will be back some day to purchase the relationship-ending potion. Diana will drink the first drink and be obsessed with Alan, and he will eventually give her a chaser beverage to end her life and obsession. The chaser-drink connotation and how it applies to the story is always an eye opener for my students. They usually have a different connotation for what "the chaser" means. Students often explain that they thought the chaser refers to a person. "The chaser" is someone that chases. This thinking actually works for this story too. Alan is the chaser that is chasing Diana, and he is willing to drug her in order to catch her.