In a medium saucepan, combine the cranberries, chicken broth, honey, balsamic vinegar, and thyme. Bring to a boil, then reduce the heat and let it simmer for about 10 minutes until the cranberries burst and the sauce thickens slightly. Remove from heat and set aside.
Season both sides of the chicken breasts with salt and pepper.
Heat olive oil in a large oven-safe skillet over medium-high heat. Add the chicken breasts and sear them for about 3-4 minutes on each side until golden brown.
Once the chicken is browned, pour the cranberry sauce over the chicken in the skillet.
Top each piece of chicken with slices of Brie cheese, allowing it to melt as it cooks.
Transfer the skillet to the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (75°C).
Once cooked, remove from the oven and let it rest for a few minutes before slicing.
Serve the chicken drizzled with the remaining cranberry sauce and garnished with fresh parsley.