Prepare grill or broiler. Place chicken on grill rack or broiler pan coated with cooking spray, and grill or broil 45 minutes or until chicken is done, turning frequently. Let cool slightly. Remove chicken from bones, reserving bones. Cut chicken into bite-size pieces; set aside.
Combine chicken bones, Corn Stock, and next 5 ingredients (Corn Stock through sliced onion) in a large Dutch oven. Bring to a boil; reduce heat, and simmer, uncovered, 1 hour. Remove from heat. Strain mixture through a sieve into a large bowl; discard solids. Set stock aside.
Heat olive oil in pan over medium-high heat. Add Grilled Corn Kernels, red onion, cilantro, and garlic; sauté 3 minutes. Add chicken, stock, tomato, and next 5 ingredients (tomato through 1/8 teaspoon pepper). Cook until thoroughly heated. Ladle soup into individual bowls, and top with avocado.