Paid for by the owner.
Быть оплаченным владельцем; "за счет заведения".
At the opening of the new hotel, the champagne was on the house.
Oscar was the first customer at the diner, so his lunch was on the house.
You are our favorite client, the dinner is on the house.
Вы наш любимый клиент, обед за счет заведения.