Grate the cucumber and squeeze out excess moisture using a clean kitchen towel.
In a medium bowl, whisk together the Greek yogurt, squeezed cucumber, minced garlic, chopped dill, lemon juice, olive oil, salt, and pepper. Set aside or refrigerate.
Season the chicken breasts with a pinch of salt, pepper, and a squeeze of lemon juice. Grill over medium-high heat for 6-7 minutes per side until fully cooked (165F internal temperature). Let rest, then slice.
Assemble the bowls by dividing the sliced chicken, cherry tomatoes, red onion, Kalamata olives, and feta cheese into serving dishes.
Drizzle the prepared yogurt cucumber dip generously over the bowls before serving.