Place skinless, boneless chicken breast halves between 2 sheets of plastic wrap; pound to 1/2-inch thickness. Sprinkle chicken with 1/2 teaspoon salt and 1/4 pepper. Heat a large skillet over medium-high heat. Add 1 tablespoon olive oil to pan. Add chicken, sauté 3 minutes on each side or until done. Transfer chicken to a serving platter. Add 1/4 cup chicken broth, 3 tablespoons apricot preserve, and soy sauce to the pan. Bring to a boil. Stir. Cook 1 minute. Remove from heat; stir in lime juice and chile paste. Spoon over chicken; garnish with fresh cilantro leaves.
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