Preheat oven to 425°F (Gas Mark 7). In a large bowl whisk together flour, ¼ cup sugar, baking powder, baking soda and salt. Add butter and using a pastry cutter or your fingers, cut butter into flour mixture until it resembles coarse cornmeal.
Stir in strawberries, then gently incorporate Chobani, taking care not to over mix.
Turn dough onto a heavily floured work surface. Fold dough on top of itself to knead, 3 to 4 turns, then pat into 1½-in thick rectangle. Fold rectangle into thirds and shape into a 1-in thick circle. Cut into 8 wedges.
Arrange wedges on parchment paper-lined baking sheet and sprinkle tops of scones with remaining 2 T sugar. Bake until golden brown, 12 to 15 minutes. Cool on a wire rack before serving.