1. Make filling: Melt butter in a large skillet over medium-high heat. Add onion and celery; cook, stirring often, until softened, 3 to 5 minutes. Add flour and stir for 1 minute. Pour in broth and increase heat to high. Boil, stirring and scraping bottom of skillet, until mixture is thick, about 1 minute. Reduce heat to medium-low and stir in half-and-half. Add chicken and cook until firm, turning once or twice, about 5 minutes. Season with salt and pepper. Pour into a 2-quart baking dish.
2. Preheat oven to 425°F; line a large baking sheet with foil. Make biscuit topping: In a food processor, combine flour, baking powder and salt. Pulse briefly to mix. Add butter and pulse until mixture resembles coarse meal. With machine running, add 1 cup buttermilk all at once. Add chives and process just until dough forms a ball. Turn out onto a floured work surface and knead for about 10 seconds. Roll out to 1/2-inch thickness. Use a 2-inch cookie cutter to form biscuits. Gather dough, roll out and cut out more biscuits (you should have about 16 total). Place on top of filling. Brush biscuits with 2 Tbsp. buttermilk. Place baking dish on lined sheet and bake until filling bubbles and biscuits are lightly browned, about 25 minutes. Serve hot.
Make It Ahead: Prepare the filling through Step 1 up to two days in advance. Cover and chill. Bring to room temperature before proceeding. To Freeze: Make the pie but do not bake. Freeze uncovered until firm, then wrap in plastic wrap and foil and return to freezer. To reheat, uncover, re-cover in foil and bake at 375ºF for 1 hour. Raise heat to 425ºF, remove foil and bake 20 minutes longer, until filling bubbles and biscuits are lightly browned.