Cut the limes in half and squeeze the juice into a blender, scraping out some pulp as well. Add Tajín, tequila blanco, triple sec (or Grand Marnier), cold water, sugar, and ice into the blender.
Blend until smooth.
Dip the rims of 4 margarita glasses into the Chamoy to rim them.
Pour the margarita mix into the glasses and garnish with tamarind-chile straws, if desired.
Serve and enjoy!