Dice the chicken into roughly bite-sized pieces and slice the sausage. Dice the onions, peppers and celery, all relatively small. Finley chop or crush the garlic.
Warm the oil in a wide, heavy based dish then add the chicken and brown all over. Once cooked through, remove from the pan and set aside. (If you prefer, you can briefly cook the shrimp now too and set those aside, but it also works to add at the end and cook in the rice and last of the liquid). Add the Andouille sausage and brown lightly all over, a couple minutes.
Once the sausage is gently browned, add the onion, pepper and celery. Cook, stirring now and then, for a couple minutes then add the garlic. Cook until all of the vegetables are softened, around 5 minutes or so.
Add the thyme, oregano, paprika, cayenne and tomato paste. Cook for a minute or two then add the crushed tomatoes and stock. Bring to a simmer then add the rice and bay leaf. Reduce the heat and leave approximately 20 minutes until the rice is just cooked, stirring now and then.
Add the shrimp when the rice is almost cooked, pressing them under the rice mixture to help them cook through, and add back the chicken. Turn them over if needed and once the shrimp are cooked through, serve.