Make the pizza dough: In a small bowl, combine the cool water with the olive oil, honey, and salt. In another small bowl, dissolve the yeast in the warm water and set aside in a warm place for 10 minutes.

Pulse the 3 cups of flour in a food processor. With the machine on, slowly add the honey mixture. Pour in the dissolved yeast and process until the dough forms a ball. If the dough is tacky, add a little more flour.

On a lightly floured surface, knead the dough until smooth. Transfer to a buttered bowl, cover with plastic wrap, and let rest for 30 minutes.

Divide the dough into 4 pieces and roll each piece into a smooth, tight ball. Transfer the balls to a baking sheet, cover with a damp towel, and refrigerate until chilled, or for up to 4 hours. Bring to room temperature before baking.

Make the pizza: Preheat the oven to 500°F. Set a pizza stone in the oven for 30 minutes.

Knead 1/2 teaspoon of the chives into each ball of pizza dough. On a lightly floured work surface, roll each ball into an 8-inch round. Brush each round with 1 tablespoon of olive oil, leaving a 1-inch unbrushed rim. Transfer the rounds to a lightly floured baker's peel or the back of a flat cookie sheet dusted with flour. Slide the rounds onto the hot pizza stone and bake for 8 to 10 minutes, or until golden brown.

Spread the pizza crusts evenly with the crème fraîche and top with the sliced smoked salmon. Place a heaping tablespoon of caviar in the center of each pizza, garnish with the remaining chives, and serve immediately.