Cut the chicken and andouille into bite-sized pieces and dice the onions, bell peppers, and celery.
Bring the burner to medium heat. Add the flour and oil to the pot and stir for approximately 30 minutes to make a roux the color of chocolate. The roux must be stirred continuously to prevent burning.
Once the roux is formed, stir in the chicken and andouille so they are coated with the roux. Brown over medium heat for 5 minutes, stirring frequently to keep the roux from burning.
Stir in the onion, bell pepper, and celery and brown for an additional 5 minutes.
Add the water and bouillon cubes and stir until the roux is mixed well with the water.
Bring to a boil, and season to taste. Then reduce the heat and simmer for 1 hour or longer.
Serve over rice.