Trim any excess fat from the chicken pieces and pat them dry with a paper towel. Season the chicken pieces with salt. pepper, and thyme on both sides.
Cook:
Heat a large skillet over medium-high heat. Once hot, heat up the oil. Place the chicken thighs, skin-side-down, on the skillet and sear them for 6 minutes on the first side without moving them from their spot. Flip the chicken thighs over and sear the bottom side for 3 minutes. Remove the chicken pieces from the skillet onto a plate; you'll finish cooking them later.
Leave the fat in the skillet and add the onion, garlic, and peppers. Sauté for 4 minutes, until the onions are translucent and the peppers are soft. Add the quartered tomatoes or the can of diced tomatoes with the juice and the olives (whole or sliced) and the stock to the skillet and stir to combine.
Bring the sauce to a simmer and then place the chicken pieces in the skillet, skin-side-up, along with the juices from the plate. Reduce the heat to medium-low, cover with a lid, and cook for 20-25 minutes, without opening the lid, until the chicken's internal temperature reaches 175F. Remove from the heat.
Notes
In Spain, we serve this chicken with crusty bread or some white rice and a simple side salad.