Heat the avocado oil in a Dutch oven over medium heat. Add the chicken thighs and brown about 2-3 minutes per side. (You'll need to do this in 2 batches).
Remove the chicken and set aside.
With the heat still on medium, add the butter and let it melt. Then add the onion, green pepper and celery and cook about 2-3 minutes, until it starts to soften.
Sprinkle in the flour and mix to coat the vegetables well.
Slowly stir in the broth, whisking constantly. If you add it too fast without stirring, it can become clumpy.
Add the Cajun seasoning, black pepper, bay leaf and chicken and bring to a boil. Reduce the heat and simmer, uncovered, for 50 minutes.
Stir in the potato cubes and cook an additional 20-25 minutes, or until potatoes are tender all the way through.
Add salt to taste, if desired. Serve over rice or pasta, or enjoy with crusty bread.