1. Preheat oven to 425 degree F and arrange rack in center. Lightly grease 2 large cookie sheets.
2. Whisk together flour, baking powder, and salt. Add butter and, using fingertips, rub into flour mixture until it resembles coarse crumbs. Using a fork, stir in cheddar and chives until combined well. Using fork, stir in cream. Turn dough out onto a lightly floured surface and knead about 8 times, until it just holds together. Pat into a 1/2-inch-thick round, 12 inches in diameter. Using a 2-1/2-inch biscuit or flower cookie cutter, cut out shapes. Repeat, reusing scraps, to make a total of 22 biscuits.
3. Arrange biscuits 1 inch apart on prepared cookie sheets, brush tops with cream and bake until golden brown, 12 to 15 minutes. Transfer biscuits on sheets to a rack and cool 5 minutes. Using a metal spatula, transfer biscuits to rack and cool to lukewarm. Serve warm or at room temperature. Makes 22 biscuits.