My husband has been making omeletes for years, and they were always tough and over-cooked. He hates to be told what to do, insisting that if I don't like the way he does it, I should do it myself.
I finally found a recipe in an old Ladie's Home Journal Cookbook, got him to follow it, and we had the best omelets ever.
First of all, you need a good, non-stick 8" skillet with rounded sides. Use good fresh eggs, don't overbeat, and don't use too many eggs in a single omelet. (2-3 is about right.)
Have your fillings ready before you begin the omelet.
Beat the number of eggs you want slightly, with a fork, and add 1 scant tablespoon of water per egg. You can use milk or cream, but water makes the most tender omelet.
Season with a good pinch of salt, and a small pinch of pepper if you wish. You may wait to season the eggs until just before they're finished. (best, I think.) Put 1 rounded tablespooon butter into a hot pan and let sizzle, but not brown. Swish butter onto sides of pan. Pour in the eggs, lower heat, shake the pan with one hand,and stir with a fork in the other; let some of the egg run under the edges. When eggs begin to set, stop stirring for a minute, until bottom is firm, but not brown, and the top still creamy. Quickly loosen the omelet around the edges, add filling, tip the pan, and then fold omelet over in half with a spatula or pancke turner; slide onto a warm plate.
For your chilie cheese omelets...is it like chilie with red sauce and meat? If so, be sure to heat your canned chilie before you put in your omelet. Of it's green chilies, I'd mix them with sour cream and grated cheese before spreading on omelet. The latter would be great served with salsa.