1
general::
Express praise or commendation to someone, as in Meredith wanted to pay Christopher a compliment so she told him she liked his new haircut. This expression uses pay in the sense of ‘‘give something that is due." [c. 1700]
American Heritage Idioms
2
general::
Phrase(s): pay someone a compliment
Fig. to give someone a compliment. • Tom paid Bill a compliment when he told him he was intelligent. • Mary was very gracious when Anne paid her a compliment.
McGrawhill's American Idioms And Phrasal Verbs