You would have to go back to 2007 for the last time an Arsenal player has won the Copa America. Let's look at the history of Arsenal players who played in the Copa America.
Four players, going back to right back Nelson Vivas in 1999 from Argentina, have ever played a Copa America whilst under an Arsenal contract. Nelson Vivas was a part of Marcelo Bielsa's side who came to Paraguay for the 1999 edition and lost 2-1 to Brazil in the quarter-finals, with the opposition holding players such as Rivaldo, Ronaldo, and a young Ronaldinho, who went on to win the competition. Vivas played 69 times for the Gunners, scoring his first and only goal for Arsenal against Derby County in the League Cup as he was mainly used as backup for established full-backs Lee Dixon and Nigel Winterburn while at the North London outfit.
2004 saw the first time an Arsenal player won the Copa America with Brazilian midfielder, Edu Gaspar, who played 100 times for the current FA Cup holders and scored seven times in spell for four years. While he was also the first Brazilian to win the Premier League, he was apart of that inclusive squad that went the entire 2003-04 season unbeaten. Brazil won the final after a 2-2 draw which later went to penalties against their fiercest rivals Argentina, as Edu was one of the players who scored in the penalty shootout in Peru.
Further glory with Brazil
In 2007, two fellow Brazilians won the Copa America again: Gilberto Silva and Júlio Baptista, who was on loan to the Gunners from Real Madrid. Silva, who was apart of the Invinicbles as well in 2003-04, was the captain of the winning side and, this time in Venezuela, saw his side beat Argentina yet again by a score of 3-0 with an Argentina side filled with the likes of Messi, Tevez, Riquelme, Crespo, Zanetti and Veron.
Baptista scored three times in the competition, including a goal in the final against Argentina as he became the third player ever to win a Copa America while under contract at Arsenal.
Ospina and Sanchez look become the fourth Arsenal player to win the Copa America, as both players represent countries that are depending on for glory in Chile, especially Alexis. Given his fine season at the Emirates, the former Barcelona man looks to win on home soil and Ospina, with his great performances in goal for the Gunners, will look to do the same for Colombia.