Preheat oven to 450°F. Melt butter in heavy medium skillet over medium heat. Add mushrooms and sauté until tender, about 5 minutes. Cool slightly. Blend spinach, cream cheese and chives in medium bowl. Mix in mushrooms; season with salt and pepper.
Run fingers under skin of each chicken breast to loosen, creating pocket. Spread 1/6 of cheese mixture between skin and meat of each breast. Arrange chicken breasts on baking sheet. Spread 1 tablespoon Dijon mustard over each chicken breast. Bake chicken until golden brown and cooked through, about 20 minutes. Serve immediately.
