Preheat a gas or charcoal grill on high heat. On a lightly floured work surface, roll out the pizza dough into a 12-inch diameter circle.
Place the dough directly on the grates and grill for 3-4 minutes with the lid closed until the crust has grill marks and has puffed up. Turn over the crust and grill for an additional 2-3 minutes.
Remove the crust from the grill and flip it over so the first side that was grilled is facing down. Let cool for 10-15 minutes.
Spread the crème fraiche over the crust leaving a 1-inch border. Arrange the smoked salmon on top in a single layer. Dollop small spoonfuls of caviar on the smoked salmon. Sprinkle on chives and red onions followed by drops of liquid caviar.