Set an Instant Pot or other pressure cooker to 'Sauté' mode and heat oil.
In a small bowl, combine paprika, garlic powder, ½ tsp. salt, and ¼ tsp. pepper.
Pat chicken dry with paper towels, then rub all over with seasoning mixture.
Cook chicken in pot, turning halfway through, until lightly golden, about 3 minutes per side (it won’t be fully cooked through). Transfer to a plate.
In pot, combine onion, carrot, and bell pepper; season with a pinch of salt.
Cook, stirring occasionally, until slightly softened, 3 to 4 minutes.
Add garlic and oregano and cook, stirring frequently, until fragrant, about 1 minute more.
Add ¼ cup broth, scraping up any browned bits from bottom of pot, and cook, stirring frequently, until warmed through, 1 to 2 minutes.
Add rice and remaining 1 ¼ cups broth and stir to combine; season with salt and pepper, if needed.
Return chicken to pot along with any drippings.
Cover, set to 'Pressure Cook,' and cook on High for 4 minutes.
Natural release for 10 minutes before releasing remaining pressure.
Transfer chicken to a cutting board and cut into bite-size pieces.
Transfer rice mixture to a platter and fluff rice.
Top with chicken and parsley.