Thinly slice the shallot and mince garlic. Set aside
Pat chicken thighs dry and season with salt and pepper. Rub two tablespoons of fig jam on both sides of chicken.
Heat olive oil in a large skillet over medium-high heat. Once the oil is hot, brown the chicken for 2 minutes on each side. Transfer the chicken to a plate and set aside.
Add the shallot to the skillet and cook for 1 minute. Add the garlic and stir often so the garlic does not burn.
Add remaining tablespoon of fig jam to skillet, stir, and cook for 1 minute.
Add chicken broth, balsamic vinegar, and fresh thyme to the skillet. Stir to combine and let the mixture come to a boil.
Reduce the heat to medium and add chicken to the balsamic mixture. Cover the skillet and cook until the chicken has an internal temperature of 165 degrees, about 15-18 minutes.
Transfer the chicken to a plate and spoon the sauce over it.