Preheat your oven to 425°F.
In a small bowl, whisk together the maple syrup with a pinch of salt, pepper, and a minced garlic clove if desired.
Pat the chicken breast dry and brush half of the maple glaze over it. Set aside to marinate for 10 minutes.
Toss the sliced carrots with half the olive oil, salt, and pepper. Spread them on a baking sheet.
Roast the carrots in the oven for about 20-25 minutes until tender and slightly caramelized.
While the carrots roast, season the chicken with additional salt and pepper. Sear the chicken in a hot skillet over medium-high heat for about 2 minutes per side to get a nice color.
Brush the remaining maple glaze on the chicken and finish cooking it in the oven (placed on a separate tray or with the carrots if space allows) for about 10-12 minutes until fully cooked.
For the green beans, blanch them in boiling water for 2-3 minutes, then drain. In the same skillet, heat the remaining olive oil over medium heat and quickly sauté the green beans with a pinch of salt until they turn bright green and slightly crispy, about 3-4 minutes.
Plate the chicken alongside the roasted carrots and crispy green beans. Drizzle any extra glaze over the top if desired and serve immediately.