Drizzle olive oil into skillet over medium heat. Add chopped chicken and cook for 10 minutes, stirring occasionally. Add onion, celery, and garlic; cook until onion has become translucent, about 3 minutes. Move chicken and vegetable mixture to the side of the skillet.
Add butter to the skillet and melt. Sprinkle flour into the melted butter, 2 tablespoons at a time, stirring. Add 2 cups chicken broth to the flour mixture, stirring until thickened. Add heavy cream, continuing to stir. Stir in with chicken and vegetables. Add thyme and salt and pepper, to taste.
For the Thyme Biscuits:
Whisk together flour, baking powder, baking soda, salt and black pepper in a medium bowl. Stir milk into flour mixture just until combined. Pour onto a floured surface, sprinkle thyme onto dough and lightly knead together. Using a 2-inch biscuit cutter, cut out biscuits. Gather together any scraps and cut biscuits until all dough has been used. Place all biscuits on top of chicken in the skillet, leaving about 1 inch between each biscuit. Top each biscuit with a piece of thyme (optional) and a piece of butter.
Place skillet into preheated oven and bake 20-25 minutes until biscuits have turned lightly brown.