Heat the oil over medium-high heat and add the onion. Sauté, stirring frequently, until the onion has softened, about 5 minutes.

Stir in the green bell pepper, garlic, and celery, and continue cooking for another 2 minutes.

Add the chopped raw chicken and Cajun seasoning (and red pepper flakes and hot pepper sauce if adding) and stir well.

Allow the chicken to brown for a minute or two before adding the chopped andouille sausage, brown rice, chicken broth, and diced tomatoes.

Stir well, cover, and bring everything to a full boil.

Reduce the heat to a simmer and continue cooking, covered, for 40 to 50 minutes, or until the rice is soft. There will still be a decent amount of unabsorbed liquid in the pot. Add in the peeled shrimp, and cook at a full boil uncovered for another 10 to 15 minutes, until much of the excess liquid has evaporated. 

Serve, and enjoy!

Note that the longer the jambalaya sits, the more the liquid will absorb into the rice so if it seems excessively liquidy, no worries. If you want the liquid to be fully absorbed before serving the dish, I recommend making it at least 2 hours before you plan to serve it.