Place a large skillet over medium-high heat. Add the chorizo sausage and cook, breaking it up with a spatula, until it turns dark red and is crumbly, about 7 minutes.
In the same skillet, add the diced potatoes. Cook for about 10 minutes, stirring often. Add the chopped onion, jalapeño pepper, and garlic; continue to cook until the potatoes are almost fork-tender.
Return the chorizo to the skillet with the potatoes and vegetables. Mix well and season with salt and freshly ground black pepper. Stir for an additional 2 minutes to blend the flavors.