Answer: Peru

Wild potato species are found throughout the majority of the Americas all the way from the tip of Chile up to the northern reaches of the United States. For years it was believed that modern potato varieties were domesticated independently in multiple locations across the Americas.

Thanks to modern genetic testing of the wide variety of cultivars and wild species available, we now know that potatoes are descended from a single species (in the Solanum brevicaule complex) originally found in a region that is now occupied by southern Peru and extreme northwestern Bolivia. This species was domesticated approximately 7-10,000 years ago and through centuries of selective breeding has led to the 1,000+ types of potatoes we have today.

Bonus Trivia: 99 percent of all the potatoes consumed in the entire world today are descended from varieties that originated in the lowlands of south-central Chile (replacing formerly popular varieties from the Andes).