Place the chicken thighs in a large sealable heavy-duty plastic food storage bag. Add the buttermilk, honey, olive oil, thyme, and salt. Seal the bag, turn it to mix the marinade ingredients and coat the chicken, place in a pan, and marinate in the refrigerator at least overnight or ideally for 2 days, turning the bag occasionally.

Before cooking, remove the bag from the refrigerator and leave the chicken to come to room temperature. Preheat the oven to 425°F.

Remove the chicken from the marinade, discarding the marinade. Line a rimmed baking tray with aluminum foil and place the chicken pieces on it skin side up. Drizzle a little olive oil over each piece. Roast until the chicken is nicely browned and reaches an internal temperature of 170°F to 175°F on an instant-read thermometer inserted into the thickest part not touching bone, about 35 minutes. Serve immediately.