Cook the chorizo in a medium-size skillet over medium heat. Drain on paper towels.
Preheat the oven to 375 degrees F.
Put the dough out onto a well-floured surface. Divide the dough into 4 equal pieces. Roll into 4inch circles, using a rolling pin or stretching it into circles by hand. Arrange the circles on 2 baking sheets lightly brushed with oil.
Top each pizza with tomato slices and crumbled cooked chorizo. Top with shredded cheese and sprinkle with dried oregano.
Bake until the dough is golden brown and cheese is bubbly, about 20 minutes.