Heat grill. Grill chorizo links until done. About 5 minutes per side. Place links in bun and sprinkle with cheese. Place links on the top warming rack of grill and close lid so cheese will melt. Remove and sprinkle with pico de gallo, and lettuce.
Notes
Don't confuse Spanish chorizo links with Mexican chorizo hot dog links. Spanish chorizo is a cooked cured sausage with a completely different flavor profile. Mexican chorizo is an uncooked Mexican sausage product and what is used for this taco hot dog recipe.