In a small bowl, whisk together the olive oil, lemon juice, half of the minced garlic, dried oregano, sea salt, and black pepper.
Place the chicken breast in a shallow dish, coat with the marinade, and let sit for 15 minutes.
Grate the cucumber and place it in a clean kitchen towel, squeezing firmly to remove as much excess water as possible.
In a separate bowl, combine the Greek yogurt, squeezed cucumber, fresh dill, and the remaining minced garlic to create the tzatziki sauce.
Heat a grill pan or outdoor grill over medium-high heat and cook the chicken for 5-7 minutes per side until fully cooked.
Warm the chickpeas in a small pan or microwave until heated through.
Slice the chicken and serve it over the chickpeas, topped with a generous portion of the cool cucumber tzatziki.