In a medium bowl combine the marinade ingredients. Place the chicken in a large resealable plastic bag and pour in the marinade. Press the air out of the bag and seal tightly. Turn the bag to distribute the marinade, place in a bowl, and refrigerate for 2 to 4 hours.
In a medium saucepan over medium-high heat, combine the broth, 1 tablespoon oil, and 1 teaspoon salt and bring to a boil. Add the quinoa and lemon juice and stir just until combined. Cover the saucepan, reduce the heat to low, and cook until all of the liquid is absorbed, about 15 minutes, stirring once or twice. Fluff the quinoa with a fork and transfer to a bowl. Add 1 tablespoon oil, ½ teaspoon salt, the scallions, garlic, parsley, mint, and lemon zest and stir to combine. Taste and adjust the seasoning with more salt, hot pepper sauce, and pepper, if desired.
While the quinoa cooks, prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Remove the chicken from the bag and discard the marinade. Grill the chicken, smooth (skin) side down first, over direct medium heat, with the lid closed as much as possible, until the meat is firm to the touch and opaque all the way to the center, 8 to 12 minutes, turning once or twice. Transfer the chicken to a cutting board and cut crosswise into ½-inch slices.
Spread the quinoa on a large serving platter. Arrange the chicken slices in the center of the quinoa and serve immediately.