In a nonstick pan, heat the oil over medium heat. Saute the mushrooms until soft, about 2 - 3 minutes. Add the ham; cook 1 - 2 minutes.
Add the scrambled eggs to the pan. Cook, without stirring, until the egg begins to set, approximately 1 minute.
Using a heat-resistant spatula, gently lift corner of egg; tilt pan to allow uncooked egg to flow underneath. Cook until set. Repeat the procedure until the remaining egg is cooked and no longer runny. Add the cheese and chives to the omelet. Fold the egg in half and serve.
Lightly toast the bread. Place the omelet on the bread, cut in half and serve.