3 Tbsp all-purpose flour
3/4 tsp table salt, divided
1/2 tsp black pepper, freshly ground, divided
1 pound(s) uncooked boneless skinless chicken breast, four 4 oz pieces
2 tsp olive oil
1 small vidalia onion(s), cut in half lengthwise, thinly sliced (about 2 cups)
1 cup(s) reduced-sodium chicken broth
2 Tbsp balsamic vinegar
1 Tbsp thyme, fresh, chopped, or less to taste
2 tsp butter