Whisk olive oil, lime juice, garlic, cumin, chili powder, salt, and pepper in a bowl.
Pound thicker chicken pieces to even thickness. Toss with marinade and set aside 15–30 minutes.
Preheat grill to medium-high. Clean and oil the grates.
Grill chicken 5–6 minutes per side, until juices run clear and it hits 165°F inside.
Rest chicken on a board for 5 minutes, then slice or leave whole.
Warm salsa verde in a small saucepan over low heat for 2–3 minutes.
Spoon warm salsa over the chicken. Top with cilantro, jalapeño, red onion, and cotija.
Add avocado just before serving and enjoy immediately.