Leivur Øssursson or Leif Øssursson (born ca. 980 - died before 1047) was a chieftain in the Faroe Islands, before they were taken over by Norway in 1035. Leivur's reign marked the beginning of the end of the Viking age, and the end of independence in the Faeroes.
Leivur Øssursson was the son of Øssur Havgrímsson. It is unclear when and where Leivur was born, but we know that it was before 983 when his father died at the age of 23. His birthplace was possibly Norðragøta, where his father lived with Tróndur í Gøtu in Hov. His father owned a farm at Skúvoy and other farms at Brestir and Beinir.He was married to Tóra Sigmundardóttir, the daughter of Sigmundur Brestisson and Turið Torkilsdóttir.