Season the chicken breast with half of the sea salt, black pepper, and dried oregano.
Heat a grill pan or skillet over medium-high heat with half of the olive oil and cook the chicken for 6-7 minutes per side until the internal temperature reaches 165°F.
While the chicken cooks, slice the cucumber and halve the cherry tomatoes.
In a small bowl, whisk together the lemon juice and the remaining olive oil, salt, pepper, and oregano to create a dressing.
Toss the cucumber, tomatoes, and kalamata olives in the dressing until well coated.
Slice the whole wheat pita into wedges and lightly toast or grill until warm and slightly charred.
Slice the cooked chicken into thin strips.
Arrange the sliced chicken, hummus, pita wedges, and the cucumber-tomato salad on a large platter and serve immediately.