In a large oven-safe skillet, heat 1 tablespoon of olive oil over medium-high heat. Season the chicken breasts with salt and pepper, and sear for 3-4 minutes per side, until browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining olive oil and sauté the butternut squash, red onion, and garlic for 5 minutes until they start to soften.
Add the thyme, balsamic vinegar, salt, and pepper, and stir to combine.
Place the chicken breasts back into the skillet on top of the vegetables. Transfer the skillet to the oven and roast for 20-25 minutes, or until the chicken is cooked through and the butternut squash is tender.