Cut the chicken into pieces a bit smaller than for frying. Sear them in 2 Tbs. of the oil in a large kettle or Dutch oven over fairly high heat. Keep turning the chicken pieces until they brown on the outside; they should not cook through.
Remove the chicken and reserve. Add the flour and the rest of the oil to the pot and make as dark a roux as you can. The critical instruction about making a roux is to avoid burning it. This is accomplished by constant stirring and watching the heat.
When the roux is medium-dark, turn down the heat and add the onion, bell pepper, garlic and parsley. Sauté them in the roux until the onions are clear and have begun to brown a little.
Return the chicken pieces to the pot, along with the chicken stock or water, salt, pepper, Tabasco, bay leaves, and thyme. Bring to a simmer and cook for about an hour.
Slice the andouille into one-inch-thick discs. Wrap them in paper towels and microwave them on medium power for about three minutes, to remove excess fat. Add the sausage to the gumbo pot.
Simmer the gumbo for at least another hour, up to two hours. Stir every now and then. If you plan to serve it the next day, just cook it thirty minutes, let it cool to warm, cover, and refrigerate. You might want to strip the chicken meat (see next step) while waiting for the gumbo to cool.
When you're ready to serve, remove the chicken and strip the meat off if you haven't already. Slice the chicken into bite-size pieces and return it to the pot. (You can also just leave the pieces as is if you're among family.) If you made it in advance, bring it up to a simmer for about a half-hour. Add the green onions, and simmer for another three or four minutes.
Serve over cooked long-grain rice with a pinch or two of filé at the table.