In a large Dutch oven, heat 2 tablespoons of the oil over medium-high. In a large bowl, combine chicken with oregano and cumin, and season with salt and pepper. Toss to evenly coat. In two batches, cook chicken, turning occasionally, until no longer pink (it will cook more later), 3 minutes per batch. Transfer chicken to a clean bowl.
Add the remaining 2 tablespoons oil, the onion and poblano to the pot, and season with salt and pepper. Cook, stirring occasionally, until onion is softened, 2 minutes. Add garlic and stir until fragrant, 30 seconds.
Add tomato paste and tomato, reduce heat to medium-low and cook, stirring occasionally, until most of the liquid has been absorbed and mixture is thickened, 5 minutes.
Add broth, rice, beans and corn; season with salt and pepper. Mix well, stirring to lift up any browned bits on the bottom of the pot, then add chicken on top in an even layer and pour over any accumulated juices. Bring to a simmer.
Cover, reduce heat to low and cook until rice is tender, chicken is cooked through and all of the liquid has been absorbed, 20 minutes longer.
Divide chicken and rice among serving bowls or plates. Garnish with cilantro and sliced jalapeño, if using. Serve warm, with hot sauce on the side, if desired.