Using a microwave oven or double boiler, melt together the semisweet chocolate and the butter. Set aside to cool.
In a separate bowl, combine eggs, sugar and flour. Add cooled chocolate mixture, and mix until blended. Fold in white chocolate chips.
Divide mixture evenly among ramekins and place on baking sheet. Bake until tops are shiny and cracked and chocolate beneath is hot and gooey, about 20 minutes. Place each ramekin on a small plate with a teaspoon and serve, reminding children that ramekins and chocolate are hot.