Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Cut the chicken breast into 1-inch cubes and chop the red bell pepper and red onion into similar bite-sized pieces.
In a large mixing bowl, combine the chicken, bell peppers, and onions with the olive oil, rosemary, thyme, sea salt, and black pepper, tossing until everything is well-coated.
Spread the chicken and vegetable mixture in a single layer on the prepared baking sheet and roast for 15 minutes.
While the chicken is roasting, steam the broccoli florets in a steamer basket over boiling water for 3-4 minutes until they are bright green and slightly tender.
Remove the baking sheet from the oven, add the steamed broccoli, and toss everything together before roasting for an additional 5-8 minutes until the chicken is fully cooked.
In a small saucepan, simmer the balsamic vinegar over low heat for about 5 minutes until it reduces by half and becomes a thick glaze.
Drizzle the warm balsamic glaze over the roasted chicken and vegetables just before serving.