Toast the quinoa in a dry skillet set over medium heat, stirring often, until it begins to crackle, about 5 minutes. Bring the stock to a boil in a medium saucepan set over high heat. Add the toasted quinoa to the stock and return to a boil. Cover, reduce the heat to a simmer and cook for 8 minutes.
In a small bowl, mix together the vinegar, mirin and lime juice. Add the chickpeas and vinegar mixture, stir, then cover and continue to cook until the quinoa is tender and the liquid is absorbed, 8 minutes.