Prepare the spice rub: In a small bowl, combine the cumin, paprika, coriander, oregano, cayenne, 1/4 tsp of the oil. Coat the chicken with the spice mixture, then set aside to marinate for 10 minutes.
Remove the chicken from the fridge and pat dry.
Make the yogurt sauce: Combine the yogurt, 1/4 tsp kosher salt, and lemon juice; cover and set aside.
Whip up some tomato relish: In a food processor, combine the garlic, plum tomatoes, parsley, and remaining 1/4 tsp salt and pulse to coarsely chop.
Heat a grill pan over medium heat; brush with the remaining tsp of oil. When the pan is hot, cook the chicken until the meat is cooked through, 2 to 3 minutes per side.
Warm the pitas on the hot grill, about 1 minute per side. When done, fill each pita with a chicken breast and top with tomato relish and yogurt sauce.