Spread the onion out on a paper towel set over a plate and place in the refrigerator to dry out a bit, about 30 minutes. Spread the chopped egg out on a decorative serving plate or other shallow dish. Refrigerate this too.
In a small bowl, stir together the cream cheese and sour cream. Remove the serving dish from the refrigerator, and sprinkle the onions over the eggs. Spoon the cream mixture over the onion layer, and carefully spread flat. Spread black caviar over one half of the top, and red caviar over the other half or if you are feeling creative, make a nice pattern. Cover with plastic wrap, and refrigerate for at least 3 hours before serving.