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Kukava was born in Tbilisi on June 12, 1976. He graduated from the Tbilisi State University with a degree in law. Kukava held several governmental positions since the 1990s and practiced law when he worked as a lawyer until 2003.
As a member of Conservative Party of Georgia he joined United National Movement and participated in Rose Revolution. Shortly after being elected as a member of Parliament of Georgia Kukava left UNM alongside Conservative Party and joined opposition of Mikheil Saakashvili. In 2008 he was again elected in parliament, however like other members of opposition he declared elections rigged and decided not to join parliament.
Kukava is married and has three children.