Heat a grill pan over high heat. Rub chicken breasts with oil, and sprinkle with salt and pepper.
Add chicken to the pan, and reduce heat to medium. Cook 6 minutes on each side (depending on thickness of meat) or until cooked through. Remove from pan, let sit for 5 minutes, and slice diagonally into pieces.
Combine the cucumber slices and chopped cilantro in a bowl.
Assemble the wraps just before you are ready to serve. Heat a nonstick skillet over medium heat, and heat tortillas 15-20 seconds on each side.
Spread 1 tablespoon satay sauce on each tortilla. Top each with chicken slices and 1/4 of the cucumber mixture.
Fold in sides of tortillas, and serve immediately.