Pat chicken dry and season with 1 tablespoon salt and 1 teaspoon pepper. Place in a bowl with the thyme sprigs and cover with plastic wrap; refrigerate at least 1 hour or overnight.
Heat oil in a large skillet over medium-high heat. Remove thyme from bowl with chicken, reserving thyme. Add chicken pieces to skillet and sear, turning occasionally, until golden brown all over, about 10 minutes. Transfer pieces to a platter.
Reduce heat to medium. Stir in onion (white and light green parts) and cook until softened, about 5 minutes. Add garlic and reserved thyme; cook 1 minute more. Stir in wine and bring to a simmer, scraping up any browned bits in the bottom of the skillet. Add rhubarb, honey, ½ teaspoon salt and a few grinds of pepper.
Return chicken pieces to skillet in a single layer. Cover and reduce heat to medium-low. Simmer until chicken is cooked through, 15 to 20 minutes for breasts and 20 to 25 minutes for legs and thighs, transferring chicken pieces to a platter as they finish cooking.
Whisk butter into rhubarb sauce. Taste and adjust seasoning if necessary. Spoon sauce over chicken and garnish with sliced onion greens.