Pat chicken pieces dry with paper towels. Toss with 1 tablespoon Cajun seasoning until evenly coated. Set aside at room temperature while you prep the vegetables.

Heat 1 tablespoon oil in a large deep skillet over medium-high heat until shimmering. Add chicken in a single layer and cook undisturbed for 4-5 minutes until deeply browned. Flip and cook 2 minutes more (chicken will not be fully cooked). Transfer to a plate - do not wipe the pan.

Reduce heat to medium. Add remaining 1 tablespoon oil, then onion, bell pepper, and celery. Cook 5-6 minutes, scraping up any browned bits, until vegetables soften and edges begin to caramelize. Add garlic and remaining 1/2 tablespoon Cajun seasoning; cook 1 minute until fragrant.

Stir in rinsed rice and cook 2 minutes, stirring constantly, until grains look slightly translucent at edges. Pour in chicken broth and tomatoes with their juices. Stir well, scraping bottom of pan to release any stuck bits - this prevents burning later.

Return chicken and any accumulated juices to the pan, nestling pieces into the rice. Bring to a boil, then immediately reduce heat to low. Cover tightly and simmer 18-20 minutes until rice is tender and liquid is absorbed. Remove from heat and let stand covered for 5 minutes.

Fluff rice with a fork, taste and adjust salt if needed (Cajun seasoning varies in saltiness). Scatter green onions over top. Serve with hot sauce on the side for those who want extra heat.