Whisk first seven ingredients plus 2 Tbs. oil in a 2-cup measuring cup. Pour all but 3/4 cup of mixture into a gallon-sized zipper bag. Add chicken; seal and refrigerate 30 minutes to 4 hours. Whisk 1/4 cup of oil into remaining mixture for dressing. Peel and section oranges. Sprinkle asparagus with oil, salt, pepper.
Build a fire on only one side of grill (to conserve charcoal). When coals are covered with white ash, place chicken on rack over direct heat, cover and grill until well browned, 4 to 6 minutes. Turn, cover and grill another 4 to 6 minutes. Remove chicken and add asparagus, spears perpendicular to rack. Grill 3 to 5 minutes, until well browned and just cooked through.
Remove chicken and let stand for 5 minutes or up to 1 hour. Cut, crosswise, into 1/2-inch-thick slices. Toss greens, oranges, salt and pepper with most of the dressing. Arrange salad in six shallow bowls. Place chicken and asparagus over each. Drizzle with remaining dressing.