Season both sides of chicken with 1 ½ teaspoon thyme, salt and pepper. In a large skillet, over medium-high heat add oil.
When oil is hot, but not smoking, add chicken breasts. Cook until browned, about 5 minutes. Turn chicken over and sear other side for 5 minutes.
Reduce heat to medium and continue cooking chicken, until done, about 10 more minutes. Remove chicken and transfer to serving dish, tent with foil.
Add butter to hot skillet and stir in shallots. Cook until shallots soften, approximately 2 minutes.
Stir in figs, vinegar, broth and lemon juice. Scrape up any browned bits and simmer until sauce thickens, about 3 minutes.
Pour sauce over chicken or serve on the side. Garnish chicken with remaining thyme.
Notes
Cooking Tips: For the chicken to cook faster and more evenly, you can also flatten with a mallet to make cutlets. You can also use split chicken breasts. After searing the breasts, skin side down, for 5 minutes, put in a hot oven set at 385ºF and cook until internal temperature reads 160ºF with a meat thermometer, about 10-15 minutes. Remove from oven and continue with recipe.TO STORE: Store any leftovers in an airtight container and refrigerate for up to 4 days.TO FREEZE: You can also freeze leftovers. Transfer to a resealable bag or freezer safe container and freeze for up to 4 months.