Preheat the oven to 400°F (200°C).
Make the sauce: combine 1/4 cup balsamic vinegar, 2 tablespoons honey, 1 tablespoon Dijon mustard, and 2 minced garlic cloves in a small saucepan over medium heat.
Bring the sauce to a boil, then reduce heat and simmer, whisking occasionally, until thickened and bubbly; remove from heat and set aside.
Arrange the 1 lb chicken pieces and chopped peppers and 1 medium onion on a prepared baking sheet (lightly sprayed or lined) and season with salt and pepper.
Drizzle half of the prepared sauce over the chicken and vegetables and toss on the sheet pan to coat evenly.
Bake for about 20 minutes, tossing once halfway through, until the chicken is cooked through and the vegetables are tender; total bake time may be about 20–25 minutes.
Remove the pan from the oven, drizzle the remaining sauce over the chicken and vegetables, and sprinkle with 1 tablespoon chopped fresh basil before serving.