Season the chicken pieces with salt and pepper. Warm the olive oil over medium heat and brown the chicken on both sides, about 8 minutes per side. Transfer the chicken to a towel and remove any of the white bits in the bottom of the pan. Add the onions and sauté until soft, about 5 minutes.
Return the chicken to the pot with the thyme and bay leaf. Pour the wine and chicken stock over the chicken and place in the oven, uncovered. Cook until the meat is tender, the skin is golden, and the liquid is reduced by half, about 30 minutes.
Return the pot to the stove over low heat. Stir together the wine and honey and pour in the pot. Stem and quarter the figs and place them in the pot. Bring to a boil and allow to bubble until the liquid reduces to a syrupy consistency, about 5 minutes. Serve immediately.
If you prefer, you can use a combination of chicken breasts and thighs instead of a whole chicken.