IPA: /ˈtʃeɪsər/
KK: /ˈtʃeɪsər/
A person or thing that pursues or follows something, often used to refer to someone who chases after criminals or a drink taken after hard liquor.
After the party, he had a chaser of soda to go with his whiskey.
Chaser is formed from "chase" (from Old French *chacier*, meaning to hunt or pursue) and "-er" (meaning a person who). A chaser is a person who pursues or hunts something.
Think of someone who is 'pursuing' ('chase') something — the '-er' just means a person. A chaser is someone who actively goes after something.