Combine 1/4 cup wine, mushrooms, and currants in a small saucepan; bring to a boil. Reduce heat, and simmer, uncovered, 3 minutes. Remove from heat, and set aside.
Heat 1/4 cup broth in a medium nonstick skillet over medium-high heat. Add leek and shallots; sauté 10 minutes. Add remaining wine and remaining broth; bring to a boil. Reduce heat, and simmer, uncovered, 20 minutes.
Combine milk and cornstarch in a small bowl; stir until blended. Add milk mixture and mushroom mixture to skillet; bring to a boil, and cook 1 minute, stirring constantly. Remove from heat, and stir in lemon juice and salt; set aside, and keep warm.
Prepare grill or broiler. Place chicken on grill rack or broiler pan coated with cooking spray, and cook 6 minutes on each side or until chicken is done. Spoon cream sauce over chicken.
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