A liitle more involved but easy:
2.5 c low-salt chicken stock
1 lb shrimp, peeled and deveined, shells reserved (see note)
2 t veg oil
1 t unsalted butter
4 chicken thighs
1 medium onion, peeled, finely chopped
1 rib celery, peeled, finely chopped
1/2 red bell pepper, finely chopped
1/2 green bell pepper, finely chopped
2 t fresh thyme leaves, minced (or a scant 1 t dried)
2 bay leaves (or 1 large fresh one)
4 large garlic cloves, peeled and minced or pressed
1/2 lb andouille (or other smoked sausage), 1/4'd lengthwise then sliced crosswise into 1/4" pieces
1.5 c white rice
salt
1 14oz can diced tomatoes in juice
cayenne
fresh parsley, minced, for garnish
a few scallions, white and light green parts only, finely chopped or minced, for garnish
While you're prepping the vegs and herbs: Combine the chicken stock and shrimp shells in a med pot, bring to a low boil over med-high, cover, then reduce the heat to low and simmer 10 min. Strain the shells out while pouring the stock into a large measuring cup. You should have 2.5 c stock still--make up the diggerence with water if you don't.
Melt the butter into the oil in a Dutch oven over med-high heat till the butter's foam completely subsides. Put the chicken in the pot, skin down, and cook till browned, about 5-7. Flip the chicken and brown the other side a bit, about 3 or 4 min more. Remove the chicken to a plate; reserve. Add the andouille to the pot and cook, stirring frequently, till mostly browned all over. Scoop the andoouille out of the pot using a slotted spoon; place in a bowl and reserve. Scope out the fat situation in the pot. If more than 2 T or so, drain some out.
Reduce heat to medium, add the onion, celery and bell peppers. Stir, scraping bottom of pot with your spoon, to get up the flavorful bits stuck to the bottom of the pot. Add the thyme and bay leaves. Cook the vegs till they have softened, stirring somewhat often, about 5 min.
Add the rice to the pot a good sprinkling of salt. Stir the rice till it is well coated with fat then add the reserved chicken stock and the reserved andouille. Using a large soup spoon, scoop the tomatoes out of the can--don't drain them as you go; you want some of the juice. Add cayenne to taste.
Mix the contents of the pot well then remove the skin from the chicken and place it, skinned side down, on top of the mixture, Bring to a boil over med-high heat, reduce heat to low, cover, and simmer for 15 min. Stir the pot gently, keeping chicken on top. Re-cover the pot and simmer about 10-12 min more. (Remove a piece of the chicken and cut into it to be sure it's cooked through. Simmer a few more minutes if not.) Remove the chicken and allow to cool a bit.
Scatter the shrimp over the mixture in the pot, cover, and cook till rice is done and the shrimp are cooked through, about 5 min more.
Meanwhile, using two forks, shred the chicken. Remove the bay leaves from the pot, stir in the chicken, remove the pot from the heat, wait a min or two, then serve, sprinkling each serving with parsley and scallion.
Note: If not using shrimp, simply use 2.5 c chicken stock at the time called for. If using already-peeled shrimp, combine 1.5 c chicken stock with 1 c bottled clam juice and use at the time called for.