Cut the chicken breasts into 1-inch cubes and place them in a mixing bowl.
In a separate bowl, whisk together olive oil, lemon juice, dried oregano, garlic powder, salt, black pepper, and paprika.
Pour the marinade over the chicken cubes and ensure they are well coated. Cover the bowl and refrigerate for at least 1 hour, or up to overnight.
While the chicken is marinating, prepare the tzatziki sauce by grating the cucumber and squeezing out excess moisture, then combining it with Greek yogurt, minced garlic, and fresh dill in a bowl.
Preheat the grill or grill pan over medium-high heat. If using wooden skewers, soak them in water for about 30 minutes.
Thread the marinated chicken onto the skewers, leaving space between each piece for even cooking.
Place the skewers on the grill and cook for 10-12 minutes, turning occasionally, until the chicken is cooked through and has nice grill marks.
Remove the skewers from the grill and let them rest for a few minutes.
Serve the chicken souvlaki with warm pita bread, fresh vegetables, and tzatziki sauce.