Have ready:
Heat in a Dutch oven over medium-high heat:
Add the chicken in batches, without crowding, and cook, turning once, until golden, about 5 minutes each side. Transfer to a plate. Reduce the heat to medium and add to the fat in the pot:
Cook, stirring often, until the peppers are softened, about 10 minutes. Add:
Return the chicken pieces to the pot. Bring the liquid to a simmer, cover, reduce the heat to low to medium-low, and simmer gently until the chicken is cooked through and tender (the thighs should reach 175°F and the breasts about 160°F), about 45 minutes.
Serve over: