Season the chicken thighs with half of the Cajun seasoning, paprika, oregano, salt, and a pinch of pepper. Let them rest for a few minutes while you prep the rest.
In a large skillet, heat olive oil over medium-high heat. Add the seasoned chicken and sear until browned on both sides, about 2–3 minutes per side. Remove the chicken and set aside.
In the same pan, add the butter. Sauté the onion and bell pepper until they begin to soften, about 3–4 minutes. Stir in the garlic and cook for another 30 seconds.
Pour in the rice and toast slightly, about 1–2 minutes, stirring to coat the grains with the oils and aromatics.
Add the chicken broth and remaining Cajun seasoning. Return the chicken to the pan, nestling the pieces into the liquid.
Bring to a simmer, then reduce heat to low, cover, and cook for 15–18 minutes, or until rice is tender and chicken reaches an internal temperature of 165°F (74°C). If the liquid absorbs too quickly, add a splash more broth.
Remove from heat and let rest, covered, for 5 minutes. Fluff the rice with a fork and sprinkle with sliced green onions if using.
Taste and adjust seasoning with more salt or pepper as needed. Serve warm, straight from the skillet.