Heat a large, ovenproof skillet over medium-high heat.
Add oil to pan.
Season chicken with salt and pepper.
Add chicken to pan, and cook 2 minutes on each side, or until browned.
Remove chicken from pan.
Add broth, syrup, half of thyme (1 teaspoon), and garlic to pan; bring to boil, scraping pan to loosen browned bits.
Cook 2 minutes, stirring frequently.
Add vinegar and mustard; cook 1 minutes stirring frequently.
Return chicken to pan along with any accumulated juices, and spoon sauce over the top.
Bake 10 minutes, or until chicken reaches 165F.
Remove chicken from pan.
Heat skillet over medium heat for 2 minutes, or until liquid thickens to syrup. Watch closely as sauce will thicken quickly.
Serve sauce over chicken, and sprinkle with remaining thyme just before serving.
Notes
Chicken breast halves: It's important that you use the thinly slices halves, rather than full chicken breasts in this recipe. Chicken breast halves are sometimes called thin-sliced chicken breast halves or something similar. Full breasts won't cook in the given time.
Chicken broth: I prefer to use reduced-sodium chicken broth so that I can better control the level of salt in the recipe. You can use regular broth, if you prefer.
Mustard: If you can't find stone-ground (or don't want to buy it), you can use a brown mustard or Dijon mustard.