With the pizza stone in the oven, heat oven to 450F. Heat another 15 minutes to make sure the pizza stone is fully heated.
Meanwhile, heat a medium, nonstick skillet on medium-high heat. Add the butter, cream, and Dijon, and simmer until sauce is thickened and reduced by half.
Roll out the pizza dough and transfer to the heated pizza stone. Spread the Dijon-cream sauce over. Top with the chicken, ham, chives, sun-dried tomatoes, and cheeses. Bake 15 minutes until crust is golden and cheeses are melted.