Add the spices to a mortar or spice blender and blend until finely ground.
Cut the chicken into 2” inch cubes and toss with the seasoning. Cover and refrigerate for at least 1 hour and up to overnight.
When ready to cook, heat grill or grill pan to medium-high heat. Thread the chicken onto the bamboo skewers.
Drizzle the skewers with olive oil and grill the chicken, turning occasionally, until cooked through, about 8 to 10 minutes total. Remove and set aside.
Add the lemon halves to the grill, cut side down and grill until char marks appear, about 3 minutes. Remove and set aside.
For serving:
Arrange pita bread on a platter or plates. Spread a spoonful of tzatziki on the plate and top with the chicken skewers and lemon halves. Garnish with dill and mint and serve.