Prepare the chicken by seasoning it with salt and pepper.
Heat olive oil in a large skillet over medium-high heat.
Add the seasoned chicken breasts to the skillet and sear for 5-7 minutes per side until golden brown.
Remove the chicken and set it aside on a plate.
In the same skillet, add the bourbon and deglaze the pan, scraping up any browned bits.
Add the blackberries, honey, Dijon mustard, and chicken broth to the skillet.
Return the chicken back to the skillet, spooning some sauce over the top.
Reduce the heat to low and cover the skillet, cooking for an additional 10-15 minutes until chicken is cooked through.
Serve the chicken with the sauce drizzled generously over it.