Prepare all of the vegetables so they are ready when the meat is done.
In a deep skillet or sauté pan, brown the chicken in some oil, sprinkling with creole seasoning (don't brown if using leftover cooked bird, but you can still season the meat). Remove from the pan and tear or cut the meat into bite-size pieces.
Next brown the sliced smoked sausage or andouille and then remove from the pan.
In the same pot, sauté the onion, bell pepper and celery (add some additional oil as needed) until the onions begin to turn transparent.
Add the garlic and stir through, cooking until fragrant.
While you're sautéing the vegetables, add the tomato paste and let it pincé, meaning to let it brown a little. We're going for some additional depth of flavor by browning the tomato paste; the sugar in the tomato paste begins to caramelize, deepening the flavor and color. Keep it moving so that it browns but doesn't burn.
Once the vegetables are translucent and the tomato paste achieves sort of a red mahogany color, deglaze the pan with about 2 cups of the chicken stock, scraping the bottom of the pan to mix up any browned bits, and stir until smooth, making sure the sautéed vegetables, paste and stock are combined thoroughly. It should be fairly thick. Put this into a stock pot over a medium flame.
Add the tomatoes and seasoning to taste. Cook over medium heat for about 10 minutes. Add the sausage and poultry and cook another 10 minutes. Add the rest of the stock, check the seasonings and stir in the rice combining thoroughly. Cook, covered, for about 30 minutes until the rice has absorbed all of the liquid and the rice is cooked through.
Turn the heat down to low-medium, add the seafood, and let the sauce thicken up a bit, with the pot uncovered stirring frequently for about 10 minutes. Stir thoroughly to combine all ingredients. When the jambalaya has thickened up a bit, it's done.
Serve in bowls or deep plates, garnish with fresh parsley, with bread and a good beer.