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Arrange a rack in the middle of the oven and heat to 400°F.
Place the potatoes, onion, and bell pepper on a rimmed baking sheet. Drizzle with the oil, season with 1 teaspoon of the salt and 1/4 teaspoon of the pepper, and toss to combine. Spread into an even layer, arranging the potatoes cut-side down close to the edges of the baking sheet.
Bake until the cut side of the potatoes is golden-brown, about 15 minutes. Meanwhile, combine the vinegar, honey, 1 garlic clove, and 1 sprig rosemary in a small saucepan. Bring to a boil over medium-high heat. Cook until syrupy and reduced by half, about 7 minutes. Discard the rosemary and garlic.
Remove the baking sheet from the oven. Toss the vegetables and spread back into an even layer, leaving a space in the center of the baking sheet. Place the chicken in the center and season with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Scatter the remaining garlic clove and rosemary sprigs over the chicken. Bake until a knife slides easily into the potatoes and the chicken is almost cooked through, registering 155°F on an instant read thermometer, 12 to 15 minutes.
Remove the baking sheet from the oven and turn the oven to broil. Brush the reduced marinade onto each chicken breast, then drizzle the rest over the vegetables. Broil until the chicken darkens slightly in color, is cooked, registering 165°F on an instant read thermometer, and appears glazed, about 3 minutes. Remove from the oven and let cool 5 minutes. Serve the chicken, potatoes, and vegetables drizzled with the pan juices.