Cut the chicken and andouille into bite-sized pieces and dice the onion, bell pepper, and celery.
In a large pot, add the flour and oil, and stir over medium heat for 20-30 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, celery, and garlic and brown for an additional 5 minutes, stirring frequently.
Add the water and bouillon cubes and stir until the roux is mixed well with the water. Bring to a boil, then reduce heat and lightly boil for 10 minutes.
Season to taste. Then lower the heat and simmer for 2 hours.
Serve with rice and french bread.