Melt 1 tablespoon butter in a large ovenproof skillet over medium heat. Add chicken, skin-side down, and sear both sides until golden brown. (The skin side will take much longer, in order to properly render the fat and crisp up the skin.)
Remove chicken thighs and set aside. Pour out any excess fat, but leave some in for the sauce.
Add garlic, stir until fragrant, then add brown sugar, honey, thyme, and oregano, and stir. Reduce heat to low.
Return chicken to the skillet. Coat the chicken in the sauce.
Add green beans to skillet.
Bake for 25 minutes or until chicken is cooked through.