Heat oven to 400 degrees F.
Combine ground beef, taco seasoning, and green chiles in a large bowl, mixing lightly but thoroughly. Divide beef mixture into 16 portions; shape each portion around a cheese cube, completely covering the cheese.
Beat egg white with water in shallow dish until blended. Place chips in second shallow dish. Dip each meatball into egg white mixture, then into chips to coat completely. Press each meatball with palm into a flattened nugget shape, generously coating both sides of nugget with chips.
Spray a large baking pan with nonstick cooking spray. Place nuggets in baking pan; spray tops of nuggets generously with nonstick cooking spray. Bake for 15 to 20 minutes, or until meat registers 160 degrees F on an instant-read thermometer; meat should not be pink and juices should run clear.
Meanwhile, combine sauce ingredients in small microwave-safe dish. Microwave on high for 30 seconds or until warm. Serve nuggets with sauce.