In nonstick 12-inch skillet, heat oil over medium-high heat until hot. Add chicken and sprinkle with salt and pepper; cook 7 minutes. Turn chicken over. Reduce heat to medium; cover and cook 7 minutes longer or until juices run clear when thickest part of chicken is pierced with tip of a knife. Transfer chicken to plate.
In same skillet, cook shallot 2 minutes, stirring. In a cup, mix broth and cornstarch. Add broth mixture, jam and vinegar to skillet; heat to boiling over medium-high heat. Cook sauce 2 minutes or until slightly thickened, stirring. Return chicken to skillet; heat through.