Preheat oven to 375 degrees F. Line two baking sheets with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder and salt. Stir in the chocolate chips.
Using a wooden spoon, stir the heavy cream into the flour mixture, stirring just until ingredients are moistened.
Turn the mixture out onto a lightly floured surface. Knead gently until a soft dough forms (about 2 minutes). Divide the dough into two equal balls. Working with one at a time, pat each one into an 8-inch circle and cut into 8 triangles. Transfer the triangles to the prepared baking sheets, spacing them 2 inches apart. Brush with the melted butter and sprinkle with sugar.
Bake for 20 to 25 minutes, or until lightly browned. Serve warm or at room temperature. These scones are best served the day that they are made, but can be kept in an airtight container at room temperature for up to 3 days. You can also wrap them individually in plastic wrap and place in a freezer bag to store in the freezer for up to 2 months.