Anne O'Brien, 2nd Countess of Orkney

Anne O'Brien, Countess of Inchiquin and 2nd Countess of Orkney (born Lady Anne Hamilton; 1696 – 6 December 1756) was a Scottish noblewoman and the eldest daughter of Field Marshal George Hamilton, 1st Earl of Orkney, and his wife, the former Elizabeth Villiers.

She became Countess of Inchiquin, through her marriage to her first cousin William O'Brien, 4th Earl of Inchiquin, the O'Brien, Chief of the Name, Prince of Thomond, and Lord of Dál gCais. They were married on 29 March 1720. Their daughter, Lady Mary (c. 1721–1790), succeeded her mother in the earldom of Orkney.

Their other children were:
 * William, Lord O'Brien (1725–1727)
 * George, Lord O'Brien (born 1728; died in infancy)
 * Augustus (died in infancy)
 * Murrough, Viscount Kirkwall (died 1741, in childhood), who was heir to Henry O'Brien, 8th Earl of Thomond, but died before inheriting
 * Anne (c. 1721–1808)
 * Frances (died 1740)
 * Elizabeth (died 1741)