Combine flour and 1/4 teaspoon salt; stir well. Combine oil and water; add to flour mixture, stirring just until dry ingredients are moistened. Shape dough into a ball; cover with plastic wrap. Chill 30 minutes.
Place dough between 2 sheets of heavy-duty plastic wrap. Roll to 1/8-inch thickness; remove top sheet of plastic wrap. Invert and fit pastry into a 9-inch quiche dish or pieplate; seal to edge of dish. Remove remaining sheet of plastic wrap. Prick bottom and sides of pastry with a fork. Bake at 400° for 10 minutes or until lightly browned. Cool on a wire rack.
Snap off tough ends of asparagus. Remove scales from stalks with a knife or vegetable peeler, if desired. Cut asparagus into 1-inch pieces.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add leeks, onion, and garlic; saute 3 minutes. Add asparagus; saute until asparagus is crisp-tender. Add chicken; cook until thoroughly heated, stirring often. Spoon mixture into prepared crust.
Combine milk and remaining 4 ingredients. Pour over vegetable mixture. Bake at 350° for 25 to 30 minutes or until set. Let stand 10 minutes before slicing.