Dùn Chonnuill lies north east of Garbh Eileach, the largest island of the archipelago to which it gives its anglicised name.

The first certain reference was in 1343 when the island was granted to John of Islay, Lord of the Isles along with Cairnburgh and "Iselborgh".

By 1390 his son Donald had granted half of the constabulary of Dùn Chonnuill to Lachlan Lùbanach Maclean of Duart.

Circa 1385 John of Fordun included "the great castle of Dunquhonie" in his list of Hebridean strongholds.

[4][5] The MacLeans continued to hold the island and its castle until the mid-17th century, when ownership passed to the Campbell Earls of Argyll.