Heat olive oil in a skillet over medium-high heat. Add chorizo and cook until just beginning to crisp, about 2 minutes. Add cherry tomatoes and season with a pinch of salt. Cook and stir until tomatoes soften and release their juices, about 5 minutes.
Beat eggs with salt, pepper, and paprika in a small bowl. Stir seasoned eggs into tomato mixture in the skillet. Reduce heat to medium-low and cook and stir until the eggs are set, 3 to 5 minutes.