This town of fewer than 5,000 people is pioneering a bold experiment to sustain the "language of heaven" - 140 years after Welsh settlers arrived in South America.
Since 1997, Gamain has had a teacher from Wales running free Welsh classes.
The Assembly also pays for two other teachers, in nearby Trelew and the western Patagonian town of Esquel.
"We try to use fun ways to convey the language and get them feeling comfortable speaking Welsh", says Esyllt Nest Roberts, Gaiman's current resident Welsh teacher, as she teaches 10-year-olds a poem about zoo animals.
More than 600 students have used the language scheme every year since it began, with participants ranging from age five to 85.
Project director Robert Owen Jones says: "Lots of people come who have nothing to do with Wales. Some of them have friends or a spouse who can speak Welsh, or they might belong to one of the town's Welsh choirs and want to know what they're singing."
Fifteen Welsh speakers from the region have also qualified as foreign language teachers. All have taken part in a two-month intensive Welsh language course at the University of Wales in Lampeter.
The Patagonian language programme has brought a new status to Welsh-speaking in Argentina. Camwy college, for example, is the only secondary school in the country to include Welsh in the syllabus. The town also has a fully Welsh-speaking kindergarten.
Esyllt Nest Roberts says: "Being the only native Welsh teacher can be tiring. But knowing there are people on the other side of the world who want to learn my language makes it all worthwhile."
WELSH VOICE 14