In a large bowl mix flour with yeast, sugar and salt. Stir to combine. Add water and vegetable oil and knead well until smooth and elastic. Transfer the dough to an oiled bowl, cover with plastic wrap and let it rise until doubled in size, for about 1 hour.
Preheat the oven and your baking stone or simply a baking sheet to 470F (240C).
Turn dough onto a lightly floured surface and divide into 8 pieces. Shape each into a ball.
Using a rolling pin, roll each dough ball into a circle that is about 7-8 inches (18-20cm) in diameter and 1/4-inch (6mm) thick. Don’t make them thinner or they won’t rise.
Place pieces of dough into the preheated stone or baking sheet and bake for 3 or 4 minutes. The pita should be completely puffed, and form a pocket in the center.
Wrap the pitas in a large kitchen towel to keep them soft.