In a large bowl, combine 1 Tbs. olive oil with chicken, 1/2 tsp. salt, paprika, cumin, and turmeric. Toss well and let sit at room temperature for 10 minutes.
Meanwhile, heat 2 Tbs. olive oil in a medium saucepan over medium- high heat. Add onion, garlic, and ginger, and sweat until aromatic, about 6 minutes. Add the quinoa and stir to combine. Add 2 1/2 cups water and bring to a simmer. Stir in the tomatoes, oregano, and cilantro, then cover. Remove from heat and let steam undisturbed for 20 minutes.
In a large skillet, heat remaining 2 Tbs. olive oil over medium heat. When hot, add marinated chicken and cook until golden on all sides, 3 to 5 minutes.
Fluff quinoa with a fork, and season with salt. Transfer to a large platter, top with chicken, and garnish with cilantro sprigs and olives.