With a serrated knife, cut each egg shell about 1/2-inch from the pointed end. Empty the raw eggs into a bowl and reserve. Wash the egg shells (tops and bottoms) in warm water, then turn them upside down on a towel to dry completely.
Over very low heat melt the butter in a saucepan just large enough to hold the eggs. Beat the eggs with a whisk, pour through a sieve into the warm butter, and return to the very low heat. Beat constantly with the whisk, gradually increasing the heat, until the eggs are thick and creamy, not solid.
Remove the eggs immediately from the heat and continue whisking while adding the cream, shallots, chives, salt and pepper.
Place the dried eggshells in egg cups. Using a teaspoon, carefully fill each shell 3/4 full with the creamed eggs, then finish filling each shell with 1 tablespoon of caviar. The caviar should be slightly domed on top. Place the little top of each shell on the caviar. Serve with toast.