Melt the butter in a large metal bowl set over a pan of barely simmering water. In a separate bowl combine the eggs, the cream, the salt, and the pepper, and whisk until well blended. Pour the mixture into the metal bowl and cook, stirring occasionally, for 10 minutes. Add the ham and cook, stirring, for 3 to 4 minutes more, or until the eggs are cooked through. Stir in the chives.