In a mixing bowl, combine the fresh orange juice, fresh lime juice, olive oil, minced garlic, ground cumin, oregano, salt, and pepper. Whisk everything together until it forms a smooth, fragrant marinade.
Place the skinless chicken thighs in a shallow dish or resealable plastic bag. Pour the mojo marinade over the chicken, making sure each piece is well coated. Cover and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Rinse the yellow rice under cold water to remove excess starch. In a medium saucepan, bring the chicken broth to a boil. Add the yellow rice, reduce heat to low, cover, and simmer for about 20 minutes or until the rice is tender and the liquid is absorbed. Fluff the rice with a fork and stir in the chopped fresh cilantro.
Heat a large skillet or grill pan over medium-high heat. Remove the chicken from the marinade, letting excess drip off, and place the thighs in the hot pan. Cook for 6-7 minutes on each side or until the internal temperature reaches 165°F (74°C) and the chicken is browned.
Plate the Cuban Mojo Chicken alongside a generous scoop of yellow rice garnished with extra cilantro if desired. Serve with sautéed vegetables, salad, or your favorite sides.