STIR chopped cucumber with chopped parsley, 1 tbsp each lemon juice and olive oil and 1/8 tsp salt in a medium bowl until combined.
WHISK tahini with water, 2 tbsp lemon juice and 1/8 tsp salt in a small bowl until smooth.
TOSS chicken breasts with cumin, coriander, cinnamon and 1/4 tsp salt in a large bowl until coated. Season with fresh pepper.
HEAT an extra-large non-stick frying pan over medium-high. Add 2 tsp olive oil, then chicken. Cook, stirring often, until no pink remains, 4 to 5 min. Transfer to a plate. Add remaining teaspoon of olive oil to same pan, then sliced onions and remaining 1/4 tsp salt. Cook, stirring often, until onion is brown, 4 to 5 min. Return chicken to pan and stir until warmed through, about 1 min.
DIVIDE cucumber salad and chicken among 4 plates. Drizzle with tahini sauce. Serve with pita bread, if desired.