Generously season the chicken on all sides with salt and pepper.
In the skillet, combine the butter and oil over moderate heat.
When the fats are hot but not smoking, add the chicken skin side down, and brown until the poultry turns an even golden color, about 5 minutes.
Using tongs (to avoid piercing the poultry), turn the pieces and brown them on the other side, 5 minutes more.
Carefully regulate the heat to avoid scorching the skin.
This may have to be done in batches.
When all the pieces are browned, transfer them to a platter.
Season once again with salt and pepper.
Place the onions and garlic in the fat in the skillet and sweatcook, covered, over low heat until soft but not brownedfor about 3 minutes.
Return the chicken and any cooking juices to the pan.
Add the stock, tomatoes, and tomato paste.
Cover, and cook over low heat, turning the chicken in the sauce once or twice, until the chicken is cooked through and has thoroughly absorbed the sauce, about 20 minutes.
Add the peppers and chorizo, Cover and cook over low heat just until the peppers are soft, about 10 minutes more.