It's best to feed your starter 3-4 hours prior to starting this sourdough pita bread recipe.
In a large bowl, combine the flour, sugar, and salt. Mix in the oil and starter. Add 3/4 C. water, then add the remaining water a little at a time until dough is soft and elastic.
Grease a large bowl. Place the dough in the bowl, turning to coat.
Cover the bowl with plastic wrap and allow to proof 8-12 hours (overnight) until double in volume.
Punch down, and separate into 8 equal size portions. Roll into a ball, then press into a 6-8 inch circle about 1/4 inch thick.
Cover the dough with a damp cloth and allow to rest for 10 minutes. During that time, heat your griddle to medium heat. Place your pita on top and cook on one side until dough puffs. Flip and repeat.
Allow to cool on a flat surface. Cut each round in half and stuff with your favorite fillings.