Preheat the oven to 400 degrees Fahrenheit (204 degrees Celsius).
In a small bowl, whisk together the balsamic vinegar, honey, olive oil, minced garlic, and dried thyme until emulsified.
Place the chicken thighs and halved Brussels sprouts on a large rimmed baking sheet.
Pour the balsamic glaze over the chicken and sprouts, tossing with tongs to ensure all surfaces are thoroughly coated.
Arrange the chicken and sprouts in a single layer, ensuring Brussels sprouts are placed cut-side down to maximize caramelization.
Season the tray evenly with kosher salt and ground black pepper.
Roast for 30 to 35 minutes, or until the internal temperature of the chicken reaches 165 degrees Fahrenheit (74 degrees Celsius) and the sprouts are tender with charred exterior leaves.
Remove from the oven and allow to rest for 5 minutes to redistribute juices before serving.