Preheat large, nonstick sauté pan on medium 2–3 minutes. Place 2 tablespoons oil in pan; season chicken with 1/2 teaspoon salt and pepper. Add chicken to pan; cook 12–14 minutes, turning often, or until well-browned and 165°F.
Combine vinegar, honey, and Italian seasoning in a small saucepan on medium-low. Simmer 5–6 minutes or until mixture reduces by two-thirds and thickens.
Remove tough root end from sprouts and cut in half; place in microwave-safe bowl. Cover and cook on HIGH for 4 minutes. Cut pear in half and remove core, then cut into bite-size pieces.
Add butternut squash and pears to sprouts; cover and microwave on HIGH for 4 more minutes or until sprouts are tender. Drain well. Return chicken to pan on medium-high; add remaining 1 tablespoon oil, sprouts mixture, and remaining 1/4 teaspoon salt. Cook 3–4 minutes, stirring occasionally, or until lightly browned. Slice chicken; serve over vegetable mixture and drizzle with balsamic sauce.