Preheat oven to 400°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 3 ingredients in a large bowl. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Stir in chives and cheese. Combine sour cream, milk, and egg; add to flour mixture, stirring just until moist.
Turn dough out onto a lightly floured surface; knead lightly 4 times. Pat dough into a 7-inch circle on a baking sheet coated with cooking spray. Cut dough into 10 wedges, cutting to, but not through bottom of dough.
Bake at 400° for 16 to 18 minutes or until lightly golden. Serve warm.