Caraway Chicken Breasts with Sweet-and-Sour Red Cabbage

1 teaspoon caraway seeds
1/2 teaspoon (scant) ground allspice, divided
2 skinless boneless chicken breast halves
1 tablespoon olive oil
1 slice applewood-smoked bacon, cut crosswise into 1/2-inch strips
3 cups thinly sliced red cabbage
1/3 cup sliced shallots (about 2 medium)
1/2 cup low-salt chicken broth
2 1/2 tablespoons balsamic vinegar
1 tablespoon (packed) brown sugar
Chopped fresh chives (optional)

Sprinkle caraway and 1/4 teaspoon allspice on both sides of chicken breasts. Sprinkle with salt and pepper. Heat oil in large nonstick skillet over medium heat. Add bacon; cook until crisp. Transfer to plate. Add chicken to drippings in skillet; sauté until cooked through, about 5 minutes per side. Transfer to plate; tent with foil. Add cabbage, shallots, broth, vinegar, sugar, and 1/4 teaspoon allspice to same skillet; cook over medium-high heat until liquid is reduced to glaze and cabbage is crisp-tender, 6 minutes. Mix in bacon. Season with salt and pepper. Slice chicken; divide chicken and cabbage between 2 plates. Top with chives, if desired.