Place all ingredients in bread pan of your bread machine, select Dough setting and start. When dough has risen long enough, machine will beep.
Turn dough onto a lightly floured surface. Gently roll and stretch dough into a 12 inch rope. With a sharp knife, divide dough into 6 pieces. Roll each into a smooth ball. With a rolling pin, roll each ball into a 6 to 7 inch circle. Set aside on a lightly floured countertop. cover with a towel. Let pitas rise about 30 minutes until slightly puffy.
Preheat oven to 500 degrees F (260 degrees C). Place 2 or 3 pitas on a wire cake rack. Place cake rack directly on oven rack. Bake pitas 4 to 5 minutes until puffed and tops begin to brown. Remove from oven and immediately place pitas in a sealed brown paper bag or cover them with a damp kitchen towel until soft. Once pitas a softened, either cut in half or split top edge for half or whole pitas. They can be stored in a plastic bag in the refrigerator for several days or in the freezer for 1 or 2 months.