Finely grate the cucumber and place it in a fine-mesh strainer. Press or squeeze out as much liquid as possible. The cucumber should feel moist but not dripping wet. This step prevents the dressing from becoming watery.

Pat the chicken breasts dry: Season both sides with the kosher salt and black pepper. Heat the olive oil in a 10-inch skillet over medium heat. Add the chicken and cook for 5–7 minutes per side, depending on thickness. Cover the skillet, reduce the heat to medium-low, and continue cooking as needed until the thickest part reaches 165°F (74°C).

Transfer the cooked chicken to a cutting board and let it rest for 5 minutes. This helps retain moisture. Once cool enough to handle, shred or finely chop the chicken into bite-size pieces.

In a medium bowl, stir together the Greek yogurt, squeezed cucumber, lemon juice, olive oil, garlic, fresh dill, kosher salt, and black pepper. The dressing should be thick, creamy, and easy to scoop. If it seems unusually loose, squeeze additional moisture from the cucumber.

Place the shredded chicken in a large mixing bowl. Add the red onion and parsley. Add the tzatziki dressing and fold gently until the chicken is evenly coated.

Fold in the optional feta and Kalamata olives: Taste and adjust the seasoning if needed, keeping in mind that feta and olives add additional salt.

Cover the bowl and refrigerate for at least 30 minutes. The salad will become more flavorful as the chicken absorbs the dressing.

Serve chilled in lettuce cups, pita bread, wraps, over a green salad, or alongside toasted bread.