1. Tear bread into pieces and pulse in a food processor to make coarse crumbs. Place crumbs in a shallow bowl. Add pecans to processor and pulse until finely ground; add to bowl with crumbs. Add garlic and salt and pepper to taste, stirring with a fork until well combined. Place egg whites in another shallow bowl.
2. Rinse and pat chicken dry. Working with 1 piece at a time, dip chicken in egg whites, allowing excess to drip off, then coat bread-crumb mixture, lightly patting until evenly coated. Transfer to a large patter. Repeat with remaining chicken and chill, loosely covered, 10 minutes.
3. Heat 1 tablespoon oil in a large nonstick skillet over moderate heat until hot but not smoking. Add half of asparagus, cut side down, and cook until golden brown. Turn and cook until just tender. Transfer to a serving platter; salt and pepper to taste. Repeat with remaining asparagus adding 1/2 tablespoon oil, if needed.
4. Heat 1-1/2 tablespoons oil in skillet over moderate heat until hot. Add chicken and cook in 2 batches, turning, until golden brown on both sides and cooked through, about 5 minutes. Repeat with remaining chicken and 1-1/2 tablespoons oil. Transfer chicken to serving platter and keep warm, loosely covered.
5. Heat remaining 2 tablespoons oil over moderately high heat in skillet until hot. Add capers and cook, stirring, until golden brown, about 1 minute. Remove pan from heat. Add juice and butter, stirring, until butter is melted. Season sauce with salt and pepper. Serve chicken over asparagus, drizzled with sauce. Makes 6 servings.