Melt coconut oil in a large pot over medium heat. Add diced onions and carrots; sauté until softened.
Add marjoram, flour, and seasoning packet from the rice; stir to combine.
Add rice, chicken broth, and water; bring to a boil. Cover, lower heat to a simmer, and cook for 15 minutes.
Meanwhile, in a small saucepan, over low heat, warm heavy cream and milk. Stir warm milk mixture into the soup. Add shredded chicken. Cook for an additional 15-30 minutes or until the rice is tender.