The ancestor of he clan was Shaw MacDuff, who was also the founder of he clan MacIntosh. The Shaws naturally became part of the Clan Chattan Confederation. Shaw, the 2nd Chief, was Captain of the Confederation during the Angus raid of 1391 and the combat of champions at North Inch in 1396.
In 1468, his grandson, Aedh, acquired the lands of Tordarroch in Strathnairn, founding a new branch of the clan. This became known as Clan Aedh or Ay. The Shaws also held land on Harris and the Isles.