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Sprinkle both sides of chicken evenly with 1 1/2 tsps thyme, 1/4 tsp salt and pepper.
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Heat oil in a large non-stick skillet over medium-high heat.
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Add chicken and cook for 6 minutes on each side or until no longer pink. Remove from pan and keep warm by covering plate with towel or placing in warm oven.
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Reduce heat to medium and add butter to skillet.
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Add onions and saute for 3 minutes.
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Add broth, vinegar, soy sauce and figs.
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Simmer until sauce is reduced to 1 cup (about 3 minutes).
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Add 1 tablespoon thyme and 1/4 tsp salt.
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Cut chicken breasts on the diagonal into slices. Serve sauce over chicken.