Sprinkle chicken evenly with 1 tsp. salt and 1/2 tsp. pepper. Grill, covered with lid, over high heat 6-8 minutes on each side or until done. Let stand 15 minutes; cover and chill at least 30 minutes.
Slice hard cooked eggs in half lengthwise; carefully removed the yolks, keeping egg white halves in tact. Reserve yolks for another use.
Stir together mayonnaise, next 4 ingredients and remaining 1/2 tsp. salt in a large bowl.
Shred chicken finely and mix in to the mayonnaise mixture until blended. Spoon mixture evenly into egg white halves. Cover and chill at least 1 hour. Makes 48 appetizers. *(the recipe does not call for this, but I crumble the yokes over the tops of half the eggs)