In a medium bowl, combine the blackberries, bourbon, honey, soy sauce, apple cider vinegar, garlic, and ginger. Mash the blackberries slightly with a fork to release their juices and mix well.
Season the chicken thighs with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat. Add the chicken thighs and sear for about 4-5 minutes on each side until golden brown.
Pour the blackberry bourbon sauce over the chicken in the skillet. Reduce the heat to medium-low and cover. Cook for an additional 15-20 minutes, or until the chicken is cooked through and the sauce has thickened.
Remove the skillet from heat and let it rest for 5 minutes. Serve the chicken topped with the sauce and garnish with chopped green onions.