In a large mixing bowl, combine ground chicken, crumbled feta, red onion, garlic, parsley, oregano, lemon juice, salt, and pepper.
Gently mix ingredients by hand until just combined, avoiding overworking the meat.
Divide the mixture into 4 equal portions and shape into patties approximately 1/2 inch thick.
Preheat a grill or non-stick skillet over medium-high heat and lightly coat with oil.
Cook patties for 5 to 6 minutes per side, or until the internal temperature reaches 165°F (74°C).
Toast the burger buns lightly on the grill or in a toaster.
Spread tzatziki sauce on the bottom bun, layer with spinach, the cooked chicken patty, and a tomato slice.
Place the top bun on the burger and serve immediately.