Set a large deep skillet with a lid over medium-high heat so the pan is hot by the time the chicken is ready.

Put the chicken pieces on a plate or small tray. Sprinkle them with 1 teaspoon of the Cajun seasoning, 1/2 teaspoon of the salt, and 1/4 teaspoon of the black pepper.

Add the olive oil to the hot skillet and let it heat for about 30 seconds, until it looks loose and glossy.

Add the chicken to the skillet in one layer. Cook without stirring for 4 minutes, until the first side has good brown color.

Turn the chicken pieces with tongs or a spoon. Cook for 2 minutes more, until the second side is lightly browned but the chicken is not fully cooked through.

Transfer the chicken to a clean plate. Leave any browned bits and oil in the skillet.

Reduce the heat to medium. Add the onion, bell pepper, and celery to the skillet.

Cook the vegetables for 5 minutes, stirring now and then, until they soften and the onion starts to look clear.

Add the garlic to the skillet. Stir for 30 seconds, just until it smells fragrant.

Add the drained rice, the remaining 1 teaspoon Cajun seasoning, the remaining 1/2 teaspoon salt, and the remaining 1/4 teaspoon black pepper to the skillet.

Stir the rice in the skillet for 1 minute, until the grains look shiny and are well coated with the oil and seasonings.

Pour the chicken broth into the skillet. Use a wooden spoon to scrape the bottom of the pan so the browned bits mix into the liquid.