In a medium bowl, add tomatoes without the juice; reserve the juice. Gently crush them with your hands and using a slotted spoon, scoop the tomatoes over to another bowl; reserve this juice as well.
In a large saucepan over medium heat, add oil. When it shimmers, add onions and celery; sauté for 3 minutes. Add red peppers and cook for 3 minutes as well. Add garlic and sauté for only 1 minute. Add chicken and cook until no longer pink - at this stage, it might need more oil to prevent it from burning.
Stir in ham and sausage before adding the rest of the ingredients; rice, reserved tomato juice (*see footnote), broth, crushed tomatoes, paprika, chili powder, cayenne pepper, Worcestershire sauce, thyme, basil, gumbo file, hot sauce, sugar and jalapeño peppers.
Stir well and bring to a boil. Cover, reduce the heat to medium-low and simmer for 15 to 18 minutes or until most of the liquid is absorbed and the rice is tender.
Remove from the heat, stir and let it rest for 5 minutes before serving.
Notes
Footnote #1: I usually get about 1 1/4 cups of tomato juice from the can therefore I top it up with 1 1/4 cups of broth. As long as the total equals 2 1/2 cups of liquid.Footnote #2: Normally, I put the largest measurement amount and work my way down the ingredient list. In this recipe, I'm all over the place...sorry about that!Footnote #3: I put 15 Pickled Jalapeño in this recipe but if you want it milder or with more heat, adjust accordingly.