In 10-inch skillet, melt butter over medium heat. Cook onions and sugar in butter 20 to 25 minutes, stirring frequently, until deep golden brown and caramelized; stir in thyme leaves.
Heat gas or charcoal grill. Spread cream cheese evenly over pizza crust. Top with Alfredo sauce, shredded chicken and onions, in that order.
Place on grill over medium-low heat. Cover grill; cook 8 to 10 minutes or until hot. Avoid the temptation to grill the pizza at a higher grill temperature. The crust will burn before the toppings heat through. NOTE: When it's not nice enough to grill outdoors, I put the pizza on a pizza stone and stick it in a 450 degree oven for 8-10 minutes.
For extra flavor, substitute garlic-and-herbs spreadable cheese for the cream cheese.