Cook rice according to directions on package; set aside.
Add broth to a large pot and bring to boil over a medium heat. You can add salt and pepper to season. Be careful to not over salt. You can always add additional seasoning at the end of cooking.
Remove any skin and excess fat from chicken pieces; sprinkle pieces with seasonings (salt, pepper, garlic powder,and everglade seasoning).
NOTE: If you have chicken skin you can cook/fry it down in a seperate skillet for the grease that can be used later to make a roux that will thicken the soup.
NOTE: Don't bypass this step. Searing the chicken (most especially the breast) will make it nice and moist in the end. Heat oil in large skillet over medium high heat. Add the seasoned chicken pieces and brown on all sides. Once browned, remove from skillet and add to boiling broth. (NOTE: Reserve drippings from skillet to saute veggies). Continue cooking chicken in broth until it is cooked through and tender.
Once chicken is cooked and tender, remove from broth and set aside until cool enough to handle. Cut into bite size pieces, discarding any bones. Return chicken pieces back to hot broth.
Meanwhile; add chopped vegetable (onions, carrots, celery and garlic) to hot skillet; saute until onions are tender.
With slotted spoon, remove veggies from skillet (again reserving any drippings) and add to broth. Add thyme and mushrooms to broth. Continue cooking until carrots are tender.
To the skillet add additional oil/grease to have about 3 to 4 tablespoons of oil/grease in skillet. Heat over a medium heat. When oil is hot, add flour; whisk to make a smooth paste. Add cream and continue whisking. As roux/gravy thickens, ladle some of the broth from pot into gravy. Continue whisking until smooth and thickened. Pour gravy/roux into hot broth. This will thicken the soup making it a creamy soup. If you don't want a creamy soup, you can leave this step out.
Add cooked rice to soup, continue to heat another minute or 2 and then serve with your favorite bread. We love a nice crusty roll.
NOTE: You can used pre-cooked chicken if you like. Chicken you've picked up at the deli or oven roasted would work well. If you use pre-cooked, add it to the soup when you add the rice.