Preheat the oven to 375°F.
In a large, oven-proof skillet (about 12 inches wide), heat the oil over medium heat. Season both sides of the chicken thighs with salt and pepper. Once the oil is shimmering, add the chicken to the pan skin-side down. Sear until the skin is deeply golden brown, about 4 minutes. Transfer the chicken to a plate and set aside.
In the same pan, combine the bell peppers, shallots and chile and sauté until they develop some color and begin to soften, 5 to 7 minutes. Add the tomatoes and season everything with salt and pepper to taste. Cook until the tomatoes have just begun to soften, about 2 minutes.
While the tomatoes cook, in a small bowl or measuring cup, combine the stock, honey, balsamic vinegar and red wine vinegar and stir.
Add the honey and vinegar mixture to the pan, nestle the chicken among the vegetables and add the basil. Bring the mixture to a boil, then transfer the pan to the oven. Roast until an instant-read thermometer inserted in the thickest part of the chicken registers 165°F, 25 to 27 minutes.
Garnish with parsley and serve.