Place a chicken breast on a cutting board.  With one hand, press on top of the chicken breast. Insert the tip of a sharp knife into the side of the thickest part of the chicken breast.  Cut a slit about 3 inches long and about 3/4 of the way through the chicken breast creating a pocket.  Do not cut too deeply or all the way through.  Repeat with the remaining chicken breasts.

Pat the chicken breasts with a paper towel to remove moisture. 

in a small dish combine the salt, pepper and paprika together.   

Hold the chicken breast with the pocket facing up, open the pocket and sprinkle with the half of the seasoning and some of the thyme leaves.  Repeat with the remaining chicken breasts; then set aside. (The chicken breast will be slippery and a paper towel in your hand under the chicken is helpful.)

Preheat the oven to 425°F and line a baking sheet with parchment paper.

In a medium size skillet, melt 2 tablespoons of the butter over medium heat.  Add the sliced shallots and sauté lightly until soft, about 4 minutes; then add the garlic and cook until fragrant.    Remove from the heat and allow to cool for 5 minutes.  

Spoon a portion of the shallot mixture into each pocket, add cubes of Brie cheese and several pieces of fig.  Secure the pocket with wooden skewers or toothpicks and place on the lined baking sheet.

Melt the remaining 2 tablespoons of butter, pepper jelly and the vinegar in a small dish in the microwave and brush over the top and sides of the chicken breasts.  

Sprinkle the remaining salt/pepper/paprika mixture over the chicken breasts and transfer the baking sheet to the oven.  

Bake for 18-20 minutes until the internal temperature reaches 160°F when tested with an instant-read thermometer.  Remove from the oven, tent and allow to rest for 5 minutes.  The residual heat will continue cooking the chicken to the safe internal temperature of 165°F.