Promise to pay (3)
I believe the answer is:
'promise to pay' is the definition.
(I owe you, a promise to pay a debt)
This is all the clue.
(Other definitions for iou that I've seen before include "I owe you" , "Proof of debt" , "Admission of liability" , "Debt note (abbr.)" , "Chit acknowledging debt" .)