Cook the chicken
Season the chicken with salt and pepper. In a large frying pan over medium-high heat, warm 2 tablespoons of the oil. Add the chicken and cook, turning once, until golden brown on both sides, about 7 minutes total. Transfer to a plate.
Cook the vegetables
Add the remaining 2 tablespoons oil to the pan over medium-high heat. Add the bell peppers and onion and sauté until softened, about 6 minutes. Add the garlic and sauté for 1 minute.
Finish the chicken
Add the vinegar and half each of the basil and thyme and stir, scraping up the browned bits on the pan bottom. Return the chicken and any juices from the plate to the pan, spooning the peppers over the chicken. Reduce the heat to medium and simmer until the chicken is opaque throughout, 2–3 minutes. Stir in the remaining basil and thyme and season to taste with salt and pepper, then serve.