Trim the chicken breasts of fat and pound them to an even thickness to ensure even grilling. You can also slice them evenly in half widthwise for a quicker grill. Place prepared chicken in a large resealable bag and set aside.
In a small bowl, whisk together 1/4 cup olive oil, 1 teaspoon lime zest, 1/4 cup freshly squeezed lime juice, minced garlic, 2 teaspoons cumin, paprika, chili powder, and salt/pepper (I use about a teaspoon each). Once the mixture is well combined, remove about 2–3 tablespoons of it and reserve for later.
Add the rest of the marinade in the bag with the chicken. Seal the bag and knead with your hands to ensure all the chicken is well coated. Place in the fridge and marinate for at least 45 minutes and preferably 2–3 hours. Don’t marinate longer than 5 hours.
Preheat grill to medium-high (about 450°F.) Generously oil the grill (I drench a rolled-up paper towel in vegetable oil and, holding it with tongs, rub it over the grill grates. Don’t skip this step.) Husk the corn and rub olive oil over it. Sprinkle corn lightly with salt and pepper and place it on one half of the grill.
Remove chicken from marinade and season lightly with salt. Grill the chicken (on the other half of the grill), turning once halfway through grilling, about 4–6 minutes per side (until the thickest part of the chicken registers 165°F; see note 1). Baste the chicken with the reserved marinade as you grill and after flipping. Transfer chicken to a plate and cover with foil. Allow the chicken to rest for a few minutes so the juices can redistribute. As you baste the chicken, flip the corn too. Remove the corn when grilled to your liking (about 15–20 minutes, flipping around every 3 minutes).
Prepare the salsa! Dice the veggies—avocados, red onion, red pepper, and cilantro. Toss together in a large bowl. Add in remaining 2 tablespoons olive oil, remaining 1/4 cup lime juice, remaining 1 teaspoon cumin, minced garlic, and crushed red pepper flakes. Gently toss together. Slice the corn off the ears and add to the salsa. Add salt and pepper to taste. Toss again and serve over chicken.
Video
Notes
Note 1: The best way to avoid dry, flavorless chicken is to use a meat thermometer to test the temperature! Once the chicken hits 160°F, pull it off. (Carryover heat will bring it up the last 5 degrees.)Storage: Store leftover grilled chicken and avocado salsa separately. Keep the chicken in an airtight container in the fridge for up to 4 days. For the salsa, cover tightly and refrigerate for 1-2 days, but it's best fresh.