Filé powder, made from dried and ground sassafras leaves that flavor and thicken traditional gumbos, can be found in a well-stocked grocery—but is not essential, but if you do use it stir it in at the end of cooking. More importantly is getting the roux, the cooked mixture of butter and flour that thickens the stew, very deeply browned so that it gives a good gumbo a rounded deep flavor.
Add sausage to a large deep skillet over medium-high heat. Cook for 2 minutes; stir in chicken. Cook and stir 15 minutes or until chicken is no longer pink in center. Remove sausage and chicken from pan to a bowl; set aside.
Melt butter in skillet over medium heat; whisk in flour. Cook 15 to 20 minutes, whisking constantly, until a deep chocolate brown (avoid burning.) Stir in onion, green pepper, celery, garlic, and chile. Cook about 3 minutes or until softened. Stir in broth, Creole seasoning, and thyme. Bring to a boil; reduce heat and simmer 20 minutes.
Return the sausage and chicken to the skillet. Stir in tomatoes, okra, and black-eyed peas; cover pan and cook 5 minutes or until okra is tender. Stir in filé powder if using. Serve gumbo in large bowls over grits or rice, with hot sauce to taste.