This problem may be caused by a lighted doorbell. After the bell is wrung, the light will re-illuminate. When that happens it may be drawing just enough power to make the door chimes think that the button was pressed once again. This is a repeating pattern.

If a lighted door button is used, the solution is to either replace the button with a non-lighted version, or open the button and disconnect the light inside it.

Yes, I had this problem myself. I had replaced an old doorbell button with a new, lighted one. I ripped out the tiny light inside and it worked fine after that.