This name comes from the old Irish Gaelic, 'cinneidigh', literally meaning 'ugly headed'. The family came from Ireland to Celtic Dalriada, now Strathclyde, but are mainly associated with the district of Carrick in Ayrshire. They claimed descent from the Earls of Carrick and kinship to the Bruce family, whom they supported against the Comyns and throughout the War of Independence.

John Kennedy of Dunure acquired lands at Cassillis about 1360, and witnessed a charter by Robert II in 1384. His son, Sir Gilbert, was one of the hostages for the release of David II by the English in 1357. Gilbert's son, James, married Princess Mary, second daughter of Robert III. Their son, another Gilbert, was created Lord Kennedy in about 1457 and was one of the six regents during the minority of James III. A brother of the first Lord Kennedy, James Kennedy, was one of Scotland's best-loved bishops. He served briefly as High Chancellor of Scotland and was Bishop of Dunkeld, and later Archbishop of St. Andrews. At St. Andrews he founded St. Salvator's College in 1455.

Hugh Kennedy of Ardstinchar served as commander of the scots mercenary troops who fought for Joan of Arc at the siege of Orleans; hence Joan figures on the arms of Kennedy of Bargany. Sir David, third Lord Kennedy, was created Earl of Cassillis in 1509 and died at Flodden in 1513. The second Earl was murdered in 1527. Gilbert, third Earl, was one of four Scottish commissioners who were poisoned at Dieppe on their return from the marriage of Mary, Queen of Scots to the Dauphin in 1558. He had inherited his title at the age of twelve when one of his first acts was to sign, under duress, the death warrant of Patrick Hamilton, the first Scottish Protestant martyr. The fourth Earl earned an infamous reputation by 'roasting' Alan Stewart, Abbot of Crossraguel, in the black vault of Dunmore in order to obtain tracts of abbey land.