In a large stock pot or cast iron brasier, combine the tomatoes, broth or water, pepper, salt, basil, and garlic oil. Str together and place the chicken in the mixture, covering the pieces as much as possible.
Cook on medium heat, covered, for 25 minutes, stirring occasionally. Remove from heat, take out chicken and set on a plate, and blend soup with an immersion blender.
Add in coconut milk and stir to combine.
Cut up cooked chicken and add back in. Cook on medium for 5 more minutes and serve.
Top with addition basil and garlic oil if desired.