Preheat oven to 350 degrees. Line a large baking sheet with aluminum foil. Season chicken with salt, pepper and drizzle with olive oil. Place chicken on baking sheet and bake for 40-45 minutes until chicken is thoroughly cooked. Set aside until cool to touch. Shred chicken with forks and set shredded chicken aside.
Melt butter in a large pot over medium heat.
Add onions, celery and carrots and cook until tender, about 7 minutes.
Stir in garlic clove and cook for about a minute longer until fragrant.
Stir in flour until dissolved with vegetables and is paste like.
Slowly stir in half and half or milk about 1/4 cup at a time, stirring frequently until liquid thickens.
Stir in chicken broth, wild rice, Worcestershire sauce, parsley, garlic, thyme and bay leaf and season with salt and pepper.
Bring to a low boil then reduce to a simmer and cook for at least 30-40 minutes.