Veracruz sauce is traditionally served with seafood, such as red snapper or shrimp. Here, we've mixed things up with chicken thighs that bake up juicy and crisp for a dinner that's quick and easy.
Preheat oven to 450 degrees with rack in upper third. Season chicken on both sides with salt and pepper.
Toss potatoes with 2 tablespoons oil; season with salt and pepper. Arrange, shingled, in a shallow 9-by-13-inch baking dish; bake until just tender and edges are golden, 10 to 15 minutes.
Stir together tomatoes, cinnamon, and oregano; season with salt and pepper. Pour mixture over potatoes; scatter with olives, shallots, and oregano sprigs. Top with chicken and drizzle with remaining 1 tablespoon oil. Bake until chicken is browned and crisp and a thermometer inserted into thickest parts (without touching bones) reaches 165 degrees, about 25 minutes. Serve.