This one is on

this one is on (one)

This drink, meal, performance, etc., is going to be paid for by one. A: "How much do I owe you for the tickets?" B: "Nothing, this one's on me." No, no, this one is on the house—the boss insists.
See also: on, one, this
Farlex Dictionary of Idioms.

This one is on someone

the cost of this drink or meal will be paid by the person named or designated. A: Should we ask for separate checks or what? B: No, no, this one's on the boss! As the waiter set down the glasses, Fred said, "This one's on me."
See also: on, one, this
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.
See also:
  • this one is on (one)
  • IOU1
  • be in (one's) debt
  • be in somebody's debt
  • debt
  • IOU
  • Jinx, you owe me a Coke!
  • owe
  • (one's) (true) stripes
  • make up for (something)