The 21-year-old came through strongly on the final lap after lying fourth at the bell to take the silver medal in 1:18:57, with Chen finishing in 1:18:46.
"I can't believe it; I am very happy,” said Barrondo afterwards. “I have made history for Guatemala. I thank my coach and all the people who supported me and who helped me achieve this victory."
"It was a glorious day for me, but the glory is most of all for my country,” said Barrondo. "The president congratulated me on the first Olympic medal for the country. He told me that everyone had come out on the streets to celebrate the triumph."
Guatemala became the 141st National Olympic Committee to have won at least one Olympic medal and the 58th NOC to win a medal at the London 2012 Games.