Adjust oven rack to center; heat oven to 450 degrees.
Heat oil in a 12-inch skillet over medium-high heat. Saute onion until golden, 3 to 4 minutes. Add garlic; saute until fragrant, about 30 seconds. Stir in chicken, tomatoes, spinach, cheese and olives; simmer until filling is thick and moist, 5 to 7 minutes longer. Stir in salt and pepper. Transfer to a medium bowl; cool to room temperature.
Separate biscuits onto a lightly cornmeal-coated work surface. Sprinkle with cornmeal as necessary, and roll each one into a 5 inch circle. Fill each one, using a scant 2 Tbs. filling and leaving a 1/2-inch border. Fold in half and use a fork to press edges together. Place on cookie sheets lined with parchment paper. (At this point, these can be frozen up to 2 weeks.)
Brush tops with oil and Bake until golden, 16 to 20 minutes.