Very lightly grease, with butter or vegetable oil spray, one small skillet and one medium or large skillet.
Place tortillas in the larger skillet; cover top tightly with foil; place over very low heat to warm and leave covered until ready to fill.
Pour eggs into small skillet, add salt and cook over medium heat, stirring constantly, until curdles begin to form.
Add meat; continue cooking and stirring until eggs are almost done; add shredded cheese; remove from heat.
Uncover tortillas; place torn american cheese slice on each (sprinkle with chives, if desired.)
Spoon half of the egg mixture down the middle of each tortilla; fold bottom edge (about one inch at the "foot" of the filling) up; fold over one of the sides; roll folded side toward unfolded edge, keeping bottom fold tucked securely.
Place seam side down on plate (or waxed paper for travel.) Serve warm.