Set the oven to 325°F (165°C) to preheat.
Heat canola oil in a large Dutch oven over medium heat. Season the chicken generously with salt and pepper, then sear it on each side until golden brown, roughly 5 minutes per side. Once browned, remove the chicken from the pot.
Drain the liquid from the canned tomatoes into a 4-cup measuring cup, then add chicken stock to reach a total of 4 cups. Set this mixture aside and roughly chop the tomatoes.
Add the celery, onion, bell pepper (the trinity), chopped tomatoes, cayenne, bay leaves, and garlic to the Dutch oven, stirring to combine over medium heat. Then, stir in the tomato juice and stock mixture, along with the seared chicken, tasso, andouille, and rice. Bring to a gentle simmer, then cover the pot.
Place the pot in the preheated oven and bake for 30 minutes. Afterward, take it out and let the jambalaya steam, covered, for 5 more minutes.
Top with fresh scallions and a few dashes of hot sauce just before serving for an added burst of flavor.