Cut butter into flour mixture with a pastry blender until crumbly. Cover and chill 10 minutes. Stir in chives.
Add buttermilk, stirring just until dry ingredients are moistened.
Turn dough out onto floured surface, and knead 3 or 4 times, gradually adding additional self-rising flour as needed. With floured hands, pat dough into a 3/4-inch-thick rectangle (about 9 x 5 inches); dust top with flour. Fold dough over itself in 3 sections, starting with short end (as if folding a letter-size piece of paper). Repeat 2 more times, beginning with patting dough into a rectangle.
Pat dough to 1/2-inch thickness.
Cut with a 2-inch round cutter, and place, side by side, on a parchment paper-lined or lightly greased jelly-roll pan. (Dough rounds should touch.)
Bake at 425 for 13 to 15 minutes or until lightly browned.
Remove from oven; brush with 2 Tbsp. melted butter.
Note: We tested with White Lily soft-wheat self-rising flour.