Season the chicken pieces with Cajun seasoning, salt, and pepper.
Heat olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook until browned on all sides, about 5-7 minutes. Remove and set aside.
In the same skillet, add diced onion, bell pepper, and garlic. Sauté until the vegetables are soft, about 5 minutes.
Stir in the rice and toast for about 1 minute. Add the chicken broth, bring to a boil, then reduce heat. Return the chicken to the skillet.
Cover and simmer for about 15-20 minutes, or until the rice is tender and has absorbed most of the liquid.
Once the rice is cooked, reduce the heat to low and stir in the heavy cream.
Taste and adjust seasoning if necessary before serving.