Heat the oil in a large and deep pan on moderate heat and braise the chicken that you've diced ahead of time until golden (about 8-10 min).
Take the chicken bites out and braise the onion that you've diced beforehand until softened (about 4 min).
Add the cut into strips peppers, the finely chopped garlic, chopped chorizo and Cajun seasoning. Cook while constantly stirring for about 5 min.
Return the chicken bites, add the rice, then the diced tomatoes and chicken broth. Stir very well and close with a lid. Cook until the rice is ready - about 20-25 min.