In a large bowl, whisk together lime juice, lime zest, minced garlic, minced cilantro, oil, brown sugar, chili powder, ground cumin (if using), salt, and black pepper to make the marinade.
Add the chicken to the marinade and toss until fully coated; let sit 5–10 minutes while you preheat the grill or skillet to medium-high.
Grease the grill or skillet lightly with oil. Transfer the chicken to the hot surface, discarding any leftover marinade, and cook 5–8 minutes per side until cooked through and internal temperature reaches 165°F (74°C). Remove and let rest 5 minutes, then slice.
Immediately add the sliced bell peppers to the same pan and cook 3–4 minutes, stirring occasionally, until charred and slightly tender.
Allow chicken, peppers, and rice to cool to room temperature before assembling.
Divide 1 cup cooked rice into each of 4 meal-prep containers, then evenly divide the sliced chicken and cooked peppers among the containers. Close lids and refrigerate.