Heat oil in a large pot over medium-low heat. Add pancetta; cook, stirring occasionally, until golden and crispy, about 10 minutes. Transfer pancetta to a bowl with a slotted spoon; cover and set aside.
Stir red bell peppers, onion, garlic, and salt into the same pot. Cook and stir, scraping up the bits from the bottom of the pan, until softened, about 5 minutes. Stir black pepper, basil, thyme, and bay leaf into the pot. Add chicken stock and tomato paste; stir well to combine.
Nestle chicken breasts into the pot, submerging them in the stock. Increase heat to medium and bring to a low boil. Reduce heat and simmer stew until chicken is cooked through, stirring occasionally, 15 to 20 minutes. An instant-read thermometer inserted into the center of the chicken should read at least 165 degrees F (74 degrees C).
Pull chicken out of the pot and let cool until easily handled, about 10 minutes. Stir artichokes into the stew. Shred or cut up chicken into small pieces and return to pot. Simmer stew until chicken pieces are heated through, about 5 minutes. Ladle into bowls and garnish with pancetta.