In a large, heavy pot heated over medium-high heat, warm the olive oil. Add the chicken in a single layer, working in batches if necessary, and sprinkle with 1 tsp of salt (divide the salt between the batches if needed). Cook, stirring occasionally, until browned all over, about 15 minutes. Add the onion, bell peppers, garlic, cumin, chili powder, and oregano, and cook, stirring occasionally, until the vegetables begin to soften and brown in spots, about 10 minutes. Add the tomatoes with their juice, the black-eyed peas with their liquid, and the remaining 1 tsp of salt. Bring the mixture to a boil, then immediately lower the heat to a gentle simmer.
Cover the pot with the lid slightly ajar to let some steam escape. Cook, stirring occasionally and breaking up the tomatoes as you stir, until all the flavors have melded and the chicken is very tender, about 1 hour. (If you are using thighs, the meat will begin to shred.) Add the pickled jalapeno liquid, then taste the chili and add more jalapeno liquid and/or salt if needed. For enhanced flavor, let the chili cool down, cover, and refrigerate it overnight, then reheat it the next day. The flavor will be even better.
If using, set out the hot sauce, sour cream, Cheddar cheese, avocado, cilantro, pickled jalapenos, and scallions. Serve the chili piping hot.
