Place a pizza stone on the middle rack of the oven and preheat the oven to 500°F.
On a lightly floured surface, stretch or roll out the pizza dough into an 8-inch circle, with the outer edge slightly thicker than the center.
Brush olive oil over the dough and arrange the thinly sliced red onions on top of the pizza base.
Bake the pizza dough on the hot pizza stone for 8 to 10 minutes, or until golden brown and crispy.
Spread the crème fraîche or sour cream evenly over the baked pizza crust. Then, arrange the smoked salmon slices on top of the spread.
Garnish with chopped fresh chives and, if desired, a spoonful of caviar in the center of the pizza. Add a squeeze of lemon juice for brightness.