Melt the butter over medium heat in a large stockpot until foaming subsides. Slowly add the arrowroot, whisking constantly until it cooks through, and is turning golden brown, about 5-7 minutes. Stir in the garlic, onion, celery, and bell pepper and cook until the vegetables are softened, about 5 minutes. Stir in the okra and sauté, stirring occasionally, until the vegetables look like melted Nestle’s crunch bars (as my Mom would say), about 15 minutes.
Add the tomatoes, tomato paste, sea salt, cayenne, thyme, oregano and black pepper and stir for about 45 seconds until fragrant. Then add the water, chicken, wine and bay leaves. Stir to combine, turn up the heat to high and bring to a boil. Reduce to low and simmer for about 1 hour, and until chicken is cooked through.
Remove the chicken pieces from the pot and when they are cool enough, pull the meat off the bone, discard the skin, shred and add the shredded chicken back into the pot. Remove the bay leaves. Adjust seasonings to taste with salt and pepper.
Serve gumbo over rice and sprinkle with file.