Heat the oil in a large pot over medium heat. Season the chicken thighs with 1 tsp salt, ½ tsp black pepper, ½ tsp Italian seasoning, and 2 tsp paprika.
When the oil is heated, add the chicken. Cook for 7-9 minutes on each side, until an internal temperature of 165F. Remove the chicken from the pot, cut into ½-inch pieces, and set aside.
In the same pot, add the chopped onion and cook, stirring often, for 5 minutes. Add the celery and carrots and cook until the onion is translucent, about 4 minutes. Add the garlic, 1 tsp salt, ½ tsp ground black pepper, and ½ tsp Italian seasoning, and stir to combine. Add the broth, water, lemon juice, lemon zest, and dry rice. Cover the pot and bring to a boil. When boiling, reduce the heat slightly and simmer, covered, until the rice is fully cooked, about 20 minutes.
Add the coconut milk, dill, parsley, and cooked chicken. If you prefer a thinner soup, add water in ¼ cup increments. Stir to combine and simmer on low heat until you are ready to serve.
