Place a fine-mesh sieve lined with 3 paper towels over a bowl. Pour Chobani into sieve and refrigerate at least 12 hours.
Preheat oven to 350°F. Bake graham cracker crust until fragrant and golden, 7-10 minutes. Cool completely.
Discard liquid from yogurt bowl and turn yogurt into a bowl. Stir in sugar, then scrape filling into cooled piecrust. Cover and chill 2 hours. Top with berries before serving.