Peel the onion and cut into rings. Rinse the tomatoes and cut into quarters. Cut the chives into rolls. Beat the eggs with the cream and season with salt and pepper.
Melt a little butter in a small non-stick skillet, add 1/4 of the onion and sauté briefly. Add some tomatoes and a few chives and pour in 1/4 of the eggs. Cover and cook until thickened, about 5 minutes. In this manner, fry 3 more omelets. Arrange on plates and serve.