Preheat the oven to 400°F (200°C).
Make the sauce: combine the balsamic vinegar, honey, Dijon mustard, and minced garlic in a small saucepan and bring to a boil over medium heat.
Reduce the heat and simmer the sauce, whisking occasionally, until it thickens and becomes glossy, then remove from heat and set aside.
Arrange the chicken pieces, chopped bell peppers, and chunked onion on a prepared baking sheet (lightly oiled or sprayed). Season everything with salt and black pepper.
Drizzle about half of the warm balsamic-honey sauce over the chicken and vegetables and toss gently to coat evenly.
Bake on the center rack for about 20 minutes, then toss the pan contents and continue baking until the chicken is cooked through and the vegetables are tender, about an additional 5 minutes if needed.
Remove from the oven, drizzle the remaining sauce over the chicken and veggies, sprinkle with chopped fresh basil, and serve.
