Heat pecans and 2 Tbsp. butter in a large nonstick skillet over medium-low heat, stirring often, 2 to 3 minutes or until toasted and fragrant. Remove from skillet.
Sprinkle chicken with salt and pepper. Dredge in flour.
Cook chicken in hot oil in skillet over medium heat 3 to 4 minutes on each side or until golden brown and done. Transfer to a serving platter. Top with pecans.
Add chicken broth to skillet, and cook 2 minutes, stirring to loosen particles from bottom of skillet. Add brown sugar, vinegar, and thyme, and cook 3 to 4 minutes or until sugar is melted and sauce is slightly thickened. Whisk in remaining 2 Tbsp. butter. Serve sauce over chicken.