Generously season the chicken with salt and pepper.
Heat the olive oil in a large Dutch oven or pot over high heat. Add the chicken and sear until browned, doing this in batches if necessary. Once the chicken has browned, remove it from the pot and set it aside.
Leave any drippings in the pot. Add the onion and sauté until translucent. Then add the garlic and let it cook for 1 minute. Next, add the poblano peppers, bell peppers, and jalapeño pepper. Sauté for 5 minutes.
Next, add the chicken broth, diced tomatoes, rotel, tomato paste, salsa, beans, chili powder, cumin, salt, chipotle chili power, cayenne, and paprika.
Bring the mixture to a slow and steady simmer, and carefully submerge all of the chicken in the chili.
Let the chili simmer for at least an hour and a half. You want the chicken to be so tender that it falls apart easily. If it isn't falling apart, let it keep simmering. Once the chicken is ready, use tongs to remove it from the pot and dice it with a sharp knife. Return the diced chicken to the pot.
Taste test and add more spice as desired.