In a large soup pot, stir together the tomatoes, broth or water, pepper, salt, basil, and oil.
Place chicken in the pot, covering the chicken as much as possible.
Cook on medium heat, covered, for 25 minutes. Stirring occasionally. Remove from heat, remove the chicken from the liquid, and let cool on a plate.
Blend soup with a blender. Then, add in coconut milk and stir to combine.
Pour the liquid back in the pot and add the cooked chicken. Cook on medium for about 5 more minutes and serve.