O'Neill was born in Fermoy, County Cork, Republic of Ireland. She comes from an Irish republican family in Clonoe, County Tyrone, Northern Ireland. Her father Brendan Doris was a Provisional IRA prisoner and Sinn Féin councillor. Her uncle Paul Doris is a former national president of the Irish Northern Aid Committee (NORAID). A cousin, Tony Doris, was one of three IRA members killed in an ambush by the Special Air Service in 1991. Another cousin, IRA volunteer Gareth Malachy Doris, was shot and wounded during the 1997 Coalisland attack.