Preheat oven to 425 degrees F. In a food processor or blender, combine bread crumbs, walnuts and Parmesan. Season with salt and pepper. Transfer to a large Ziploc bag. In another shallow bowl, beat egg.
Season chicken with salt and pepper. Dip each breast into egg, letting excess drip off, and then place chicken in bag with crumb mixture. Seal bag and shake to coat chicken evenly.
In a large nonstick ovenproof skillet heat oil over medium heat. Add chicken and cook until lightly browned, 1 to 3 minutes. Carefully turn chicken over and put skillet in oven. Bake until chicken is golden brown and cooked through, 8 to 12 minutes.
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