1Set oven control to broil. Chop enough cucumber to equal 1/2 cup; place in small bowl (slice 8 slices from remaining cucumber for sandwiches; set aside). Stir in remaining sauce ingredients; refrigerate until ready to use.
2In large bowl, mix chicken, spinach, olives, cornstarch, oregano, garlic, salt and pepper. Shape into 4 oval patties, each about 1/2 inch thick. On broiler pan, place patties. Broil with tops about 5 inches from heat 10 to 12 minutes, turning once, until thermometer inserted in center of burgers reads at least 165°F.
3Place burgers in pita pocket halves. To serve, top each burger with tomato, cucumber slices and about 3 tablespoons sauce.