Olive Frances Gibbs, DL (née Cox; 17 February 1918 – 28 September 1995) was a British Labour politician and anti-nuclear weapons campaigner. Gibbs entered Oxfordshire politics in 1953 and became the second woman Lord Mayor of Oxford (the first was Florence Kathleen Lower). She served as Lord Mayor twice, in 1974–75 and 1981–82, stepping in the second time to replace a colleague who had died halfway through his term. She was also the first woman to chair Oxfordshire County Council. Her husband, Edmund (accountant and founder of an eponymous Oxfordshire firm) was also a councillor for some time.