Through his grandmother Ellis MacDonnell, Countess of Antrim he was descended from her father Hugh O"Neill, Earl of Tyrone and was therefore part of the extended O"Neill dynasty which had been the dominant family in Gaelic Ireland until the Flight of the Earls.
He had a young sister named Mary. Randal"s father was a leading Catholic, and supporter of James II in the Williamite War, unsuccessfully leading a force to capture Derry in 1688. However the title was restored in 1697.
Randal succeeded to the Earldom following his father"s death in 1699.
Like his father he was suspected of Jacobite leanings.
