Chanturia began his career on FC Saburtalo, and was loaned to Barcelona in June 2009. He was filled into Barça's Juvenil B squad, and scored 11 goals to help the Catalans to the league title.
In August 2010, after been linked with Chelsea, Chanturia signed with Vitesse. In April 2011 he signed a three-year deal with the club.
Chanturia made his competitive debut for Vitesse on the opening day of the 2011–12 Eredivisie season, as a starter in their 0–0 away draw against ADO Den Haag on 7 August. He scored his first goal for the Arnhem side in his second official match, against VVV-Venlo in a 4-0 win.
In December 2012, Chanturia was loaned to Alania Vladikavkaz until the end of the season. He returned to Arnhem club at the end of the season.