Prepare the chicken rub. In a small bowl, whisk together the olive oil, lime juice, lime zest, chili powder, brown sugar, salt, cumin, smoked paprika, onion powder, garlic powder, chipotle chili powder, and black pepper.
Coat the chicken. Add the chicken breasts to the rub and coat thoroughly on all sides.
Marinate. For the best flavor, let the chicken sit for about 30 minutes at room temperature if cooking immediately, or refrigerate it for up to 8 hours. If refrigerated, let it sit out briefly before cooking.
Make the salsa. Combine the tomatoes, corn, red onion, bell pepper, jalapeño, cilantro, garlic, lime juice, cumin, salt, and pepper in a bowl. Cover and refrigerate for 30 minutes to allow the flavors to blend.
Cook the chicken on the stovetop. Heat a lightly greased grill pan or skillet over medium-high heat. Add the chicken and cook undisturbed for about 3–5 minutes, until browned.
Finish cooking. Flip the chicken, cover the pan, and reduce the heat to medium. Cook for another 5–7 minutes, depending on thickness, until the thickest part reaches 165°F (74°C) on a food thermometer. USDA guidance recommends 165°F as the safe minimum internal temperature for poultry.
Or grill the chicken. Preheat a greased grill to medium heat, approximately 375–450°F. Grill the chicken for about 5–7 minutes per side, or until it reaches 165°F internally.
Rest the chicken. Transfer the cooked chicken to a cutting board and let it rest for 5 minutes before slicing.
Finish the avocado salsa. Just before serving, gently fold the chopped avocados into the prepared salsa. Taste and adjust the salt, pepper, and jalapeño seeds as desired.
Serve. Slice the Fiesta Lime Chicken and spoon the avocado salsa generously over the top. Finish with an extra squeeze of fresh lime juice if desired.