Verde Chilaquiles with Eggs

Name: Verde Chilaquiles with Eggs
Ingredients: 1 tablespoon vegetable oil; 1.5 cups thinly sliced red onion; 1 jalapeno pepper, seeded and minced; 2 (16 ounce) jars salsa verde; 1 pound shredded cooked skinless, boneless chicken breast; 1 (10 ounce) bag tortilla chips; 1 (2.25 ounce) can sliced black olives, drained; 0.25 cup chopped fresh cilantro; 8 eggs; 1 dash salt; 1 dash ground black pepper; 0.5 cup crumbled cotija cheese; 4 radishes, sliced, or to taste; 1 avocado, sliced, or to taste