Cut andouille sausage into ¼ inch slices.
Cut chicken thighs into ½ inch chunks.
Peel and small dice onions.
Clean, core, and small dice bell pepper.
Remove stem end from celery and small dice.
Peel and mince garlic cloves.
Heat stockpot over medium high.
Add oil to pot.
Once oil is hot, add sausage.
Cook while stirring, rendering the fat from the sausage, and lightly browning, about 5 minutes.
Add chicken, Continuing to stir as needed in order to sear evenly, about 3 to 5 minutes.
Add the "trinity", onion, bell pepper, and celery to the pot.
Cook while stirring until onions become translucent, about 8 minutes.
Add garlic and stir to combine.
Add shrimp and stir to combine.
Add the Cajun seasoning and stir just enough to combine and start to cook, a couple of minutes at most.
Add bay leaves.
Add hot sauce and Worcestershire.
Stir the bouillon into the water, and add to pot, increasing the heat to high.
Bring the soup to a rapid boil.
Add small amounts, (about 2 Tbsp.) of the roux to the boiling liquid at a time, allowing it to return to a boil be fore adding more, until desired thickness is acheived.
Taste and adjust seasoning if needed.
Reduce heat to a low simmer and allow to cook for about 10 minutes, stirring occasionally to prevent burning.
Serve with cooked fluffy white rice.
