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.
I tried this because it was such a strange set of ingredients -- maple syrup, balsamic vinegar, and peanut butter. I don't know who thought this one up but I had to see if it was edible. Well it was way more than edible, it was delicious. I'm going to be making this often as the ingredients are all in my cupboard. That's sooooo convenient. It's easy to make and as I already said -- delicious. My only reservation would be that I don't think it's necessary to use chunky peanut butter. Creamy would work just fine.