Remove giblets and excessive fat from chicken. Rinse chicken inside out. Pat dry with paper towels. Place beer can roaster on a baking tray and place chicken on the beer can roaster to allow it to drip dry for an hour.
Combine kosher salt, ground pepper, and dried thyme in a small bowl. Reserve 1 teaspoon dry rub mixture to season vegetables.
Remove chicken from the roaster. Discard juices and pat dry baking tray with paper towels. Liberally sprinkle or pat dry rub mixture on the inside and outside of the chicken. Place chicken back onto the beer can roaster.
In a large bowl, combine carrots, potatoes, onion, the reserved 1 teaspoon dry rub mixture, and olive oil. Mix well. Transfer onto the baking tray around the chicken.
Preheat oven to 375°F (190°C). Roast chicken on the beer can roaster for approximately 1 hour 15 minutes to 1 hour 30 minutes or until thermometer inserted into the thickest part of the thigh without touching the bone registers 180°F.
Let chicken rest for 15 minutes before carving.
If the top part browns too quickly, tent loosely with aluminum foil.