Sargissian played for Armenia in the
Chess Olympiads of 2000, 2002, 2004, 2006, 2008, 2010 and 2012. He took team bronze medal in 2002 and 2004, team gold medal in 2006, 2008 and 2012, and team silver medal em 2022. On Sargissian's performances at the Chess Olympiads, Grandmaster Peter Svidler commented in 2010: "Gabi Sargissian is a kind of Armenian Hulk: a very good, but nevertheless not brilliant player, who once every two years at the Olympiad turns into a real monster, and in many ways it was due to that metamorphosis that the Armenians twice won the Olympiad.". Svidler's comment proved to be true once again at the 2022 Chess Olympiads, where Armenia's Silver Medal was largely due to Sargissian's stellar performance in board one, where in the last decisive five rounds he scored 4.5 points, with wins over 4 grandmasters with ratings above 2700:
Caruana,
Pentala Harikrishna,
Mamedyarov and
Shirov. Armenia won its first ever
Chess Olympiad at the
37th Chess Olympiad. Sargissian played on board five for the Olympiad. The Armenia national chess team won gold ahead of China and the United States. In 2008, Sargissian won the
38th Chess Olympiad in
Dresden with the Armenia national Chess team, winning gold for the second time in a row at a Chess Olympiad. He played on board three and defeated Alexander Grischuk, the only win in a game with Russia, putting Armenia in the lead. Armenia ended up winning by one point ahead of Israel. In this Chess Olympiad, Sargissian won the gold medal for his individual performance on board three (+7 −0 =4 with an Elo
performance rating of 2869). Armenian President
Serzh Sargsyan attended the Olympiad to support the team. After the Olympiad, they flew back to Armenia with him on the presidential plane, Air Force Armenia One. Armenia and Sargissian regained their Olympiad title in 2012 at the
40th Chess Olympiad. This was the third time Armenia won gold at the Olympiad. As the players, one of them was
Levon Aronian, were awarded their gold medals, the Armenian national anthem
Mer Hayrenik was played and the Armenian flag was raised in Istanbul. Upon returning to Yerevan, the players were welcomed back with a ceremony by many people in the city the moment their airplane touched down in
Zvartnots Airport. The Armenian national chess team won the
World Team Chess Championship for the first time in 2011, the tournament took place in
Ningbo. Sargissian played on board four. Sargissian played for "CA Linex Magic Mérida" (Spain) in the 23rd
European Chess Club Cup in Kemer 2007, winning team gold medal. He played for "MIKA Yerevan" in the European Chess Club Cup in 2008, 2009, 2010 and 2011. ==Awards==