Jobava won the Dubai Open in 2003 with a score of 7 points out of 9. He took part in the FIDE World Chess Championship 2004, where he was knocked out in the first round by Ruben Felgaer. He won the 2nd Samba Cup in Skanderborg, Denmark in 2005. In 2006 Jobava won the Railyaway Hotel Cup and the prestigious Aeroflot Open.

In 2008 he tied for 1st–8th with Nigel Short, Vadim Milov, Aleksej Aleksandrov, Tamaz Gelashvili, Alexander Lastin, Gadir Guseinov and Farid Abbasov in the President’s Cup in Baku. Jobava won the silver medal in the European Individual Championship 2010, held in Rijeka. In August 2011 he tied for 1st–2nd with Hrant Melkumyan in the Lake Sevan tournament in Martuni and won the event on tie-break. In December 2011 he won the 32nd Edoardo Crespi Trophy in Milan with 8,5/9, finishing two points ahead of second placed Vladimir Malaniuk. In the same month Jobava won the European Rapid Chess Championship in Warsaw ahead of 746 players.

In January 2014, Jobava finished equal second and third on tiebreak in the Tata Steel Challengers tournament in Wijk aan Zee scoring 8.5/13. In the following month he won the David Bronstein Memorial in Minsk on tiebreak over Sergey Fedorchuk and Mikhailo Oleksienko. In July he finished second behind Wesley So at the ACP Golden Classic in Bergamo, Italy. In August, 2015, he took clear first place in the 19th HZ Chess Tournament in Vlissingen, the Netherlands, scoring 8/9 points (+7=2-0). In 2017 Jobava tied for first with Maxim Matlakov and Vladimir Fedoseev in the European Individual Championship in Minsk, taking the silver medal on tiebreak.

Team competitions

Jobava has played for the Georgian national in the Chess Olympiad since 2000.He won the individual gold medal in 2004, scoring 8½/10 points. In 2010, he defeated the world’s number one player Magnus Carlsen in the Georgia-Norway match. In 2016, he won the individual gold medal for the best first board. He considers this achievement to be his best result in his career so far.

Personal life

His younger brother Beglar Jobava is also a chess player, an International Master.