Lightly grease a large baking sheet. Set aside.
In a large bowl, combine the flour, baking powder, sugar and salt. Using a pastry blender, cut in butter until mixture resembles coarse crumbs. Stir in cheese. Make a well in center of flour mixture; set aside.
In a medium bowl, combine the 3/4 cup whipping cream, bacon and chives. Add cream mixture all at once to flour mixture. Using a fork, stir just until moistened. (If dough is too crumbly, add 1 to 2 tablespoons additional cream until dough comes together.)
Turn dough out onto a well-floured surface. Knead dough by folding and gently pressing it for 10 to 12 strokes or until nearly smooth. Pat or lightly roll into a 7-inch round, about 3/4-inch thick. Transfer round to prepared baking sheet.
Cut into eight wedges. Spread the wedges apart a little on baking sheet. Lightly brush tops with the 1 tablespoon whipping cream.
Bake in a 425° oven about 20 minutes or until golden brown. Remove scones from baking sheet; serve warm or at room temperature.