Cut the chicken breast into 1-inch cubes and place them in a medium mixing bowl.
In a small jar, whisk together the olive oil, lemon juice, dried oregano, garlic powder, sea salt, and black pepper.
Pour the marinade over the chicken cubes, toss to coat thoroughly, and let marinate in the refrigerator for at least 20 minutes.
While the chicken marinates, prepare the tzatziki by squeezing the excess moisture out of the grated cucumber using a clean kitchen towel.
In a small bowl, combine the Greek yogurt, squeezed cucumber, minced garlic clove, and chopped fresh dill; stir well and set aside.
Thread the marinated chicken cubes onto wooden or metal skewers.
Preheat a grill or grill pan to medium-high heat and lightly oil the grates.
Grill the skewers for 4-5 minutes per side, or until the chicken is charred and reaches an internal temperature of 165°F.
Serve the warm chicken skewers with the prepared tzatziki sauce and a side of halved cherry tomatoes and sliced cucumbers.