Heat 4 tablespoons olive oil and next 4 ingredients in small skillet over medium heat until herbs are aromatic, about 11/2 minutes. Pour herb oil into bowl; cool.
Heat 2 tablespoons oil in large pot over medium heat. Sauté chicken 5 minutes. Using slotted spoon, transfer chicken to bowl. Add 2 tablespoons oil to pot. Add onion, carrots, and celery; sauté until beginning to brown, about 15 minutes. Mix in last 5 ingredients. Bring to boil. Reduce heat; simmer 15 minutes. Add chicken; simmer until cooked through, about 5 minutes. Season with salt and pepper.
Ladle soup into bowls. Gently swirl 1 teaspoon herb oil into center of each.