Crumble ground beef into a large skillet over medium-high heat. Cook until evenly browned, and drain off grease. Add taco seasoning, and cook according to package directions. Set aside.
Heat 1 inch of oil in a large skillet, or preheat a deep-fryer to 375 degrees F (190 degrees C).
Lay out one egg roll wrapper at a time, and place a little more than a tablespoon of the ground beef in the center. Top with a small spoonful of green chilies, and a little bit of shredded cheese. Roll up according to package instructions, and seal edges, wetting with water if necessary. Repeat with remaining wrappers and filling.
Fry the rolls in the hot oil until golden brown on all sides, about 5 minutes. Remove from the oil to drain on paper towels. Serve hot and fresh.