Tear off a 36 x 18-inch piece of heavy-duty foil; fold in half to make an 18-inch square.
Place asparagus in center of foil; drizzle with 1 teaspoon of the oil and sprinkle lightly with salt and coarsely ground pepper.
Bring up opposite edges of foil and seal with a double fold.
Fold remaining edges to completely enclose asparagus, leaving space for steam to escape; set aside.
Brush chicken and mushrooms with remaining oil; sprinkle lightly with salt and pepper.
For a charcoal grill, place chicken, mushrooms, and foil packet with asparagus on the rack of an uncovered grill directly over medium coals.
Grill for 12 to 15 minutes or until mushrooms are tender and an instant-read thermometer inserted in chicken registers 170-176F, turning chicken and mushrooms once (For a gas grill, preheat grill. Reduce heat to medium. Place chicken, mushrooms, and foil packet on grill rack over heat. Cover; grill as above.).
Remove chicken, mushrooms, and foil packet from grill; slice mushrooms.
Toast bread slices on grill rack for 1 to 2 minutes, turning once; spread one side of each with cream cheese.
On serving plates stack half of the bread slices, spread side up, chicken, remaining bread, mushrooms and asparagus.