Sprinkle chicken evenly with salt, paprika, and thyme.
Cook chicken in hot oil in a large nonstick skillet over medium-high heat 2 minutes on each side or until golden brown. Stir in chicken broth and next 4 ingredients, and bring to a boil. Cover, reduce heat to low, and simmer 15 minutes. Remove chicken to a serving platter, and keep warm. Reserve liquid in skillet.
Whisk peanut butter into reserved liquid, and boil over medium-high heat, uncovered, 5 minutes or until sauce is thickened; spoon sauce evenly over chicken.