In a small bowl, whisk together 1 tablespoon of lime juice, lime zest, half the olive oil, sea salt, and black pepper.
Place the chicken breast in a shallow dish, coat thoroughly with the lime marinade, and let sit for 15 minutes.
In a small saucepan, combine the white rice and water; bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes until the water is absorbed.
While the rice cooks, heat the remaining olive oil in a skillet over medium heat and sauté the diced yellow onion until translucent.
Add the marinated chicken to the skillet and sear for 6-7 minutes per side until the exterior is golden brown and the internal temperature reaches 165°F.
Remove the chicken from the skillet to rest, then fluff the cooked rice with a fork and stir in the remaining lime juice and chopped fresh cilantro.
Slice the chicken into strips and serve over the cilantro rice, topped with the sautéed onions.