Portugal, Iceland and Argentina. In the following year (2010) three more countries legalized gay marriage: Portugal, Iceland and Argentina. Argentina became the first Latin American country in the world to legalize gay marriage.8. Ireland was the first country in the world to approve same-sex marriage by a referendum. Voters were asked whether to add to the Constitution that “marriage may be contracted in accordance with law by two persons without distinction as to their sex.” The referendum took place on May 22nd 2015.