Place the chicken thighs in a medium bowl. Add the oregano, salt and pepper, and toss to coat the chicken.
Heat 1 ½ teaspoons of olive oil in a large nonstick skillet set over medium-high heat. Add the chicken and cook for 2 minutes per side. Transfer the chicken to a plate.
Reduce the heat to medium. Heat the remaining 1 teaspoon of olive oil in the skillet. Add the onions and carrots, and cook until the vegetables are tender, 4 to 5 minutes.
Stir the crushed tomatoes, water and quinoa into the vegetables. Bring to a boil, then reduce heat, cover and simmer for 15 minutes. Nestle the chicken into the quinoa and cook until the liquid is absorbed and the chicken is cooked through, about 15 minutes.
Uncover, remove from the heat and let rest for 5 minutes to allow the quinoa to absorb the rest of the liquid.