Preheat a gas or charcoal grill to 400 degrees F or medium direct heat.
For each nacho packet, rip off one 2-foot long piece of heavy-duty aluminum foil (or two 2-foot long pieces of regular aluminum foil, stacked on top of each other) and lay on a flat surface. Crimp the edges of the foil up slightly to make "walls" for the packet.
Place about 1/4 of the tortilla chips on one side of the foil, leaving about 2 inches of space around the edges so you'll be able to seal the foil packet.
Top the chips with about 1/2 cup shredded cheese and 1/4 of the Velveeta cubes—be generous with the Velveeta if you like and use the other half of the block if you really want to load it on.
Fold the foil packet over to enclose the chips and cheese and crimp the edges together to seal.
Place the packet directly on the grill grates and close the lid. Cook for about 5 minutes, until the cheese is melting and the chips are starting to toast at the edges. (Be careful when opening the foil packets to peek for doneness, as steam may escape.)
Top the nachos with any or all of your favorite fixings and serve immediately.