In a 10- to 12-inch nonstick frying pan over medium-high heat, stir garlic, ginger, green onions, and oil just until onions are limp, about 5 minutes.
In a bowl, mix soy sauce with chicken. Rinse and core tomatoes; cut crosswise into 1/8- to 1/4-inch-thick slices.
Place pizza crust in a 12-inch pizza pan or on a 14- by 17-inch baking sheet. Spread crust evenly with sauce, then scatter chicken mixture and onion mixture over sauce. Sprinkle pizza with cheese, and arrange tomato slices evenly over the surface.
Bake in a 350° oven until cheese is melted and pizza is hot in center, 12 to 15 minutes. Cut into wedges.