Preheat a grill pan or non-stick skillet over medium-high heat.
Season the chicken breast with half of the sea salt, black pepper, and dried oregano.
Grill the chicken for 6 to 7 minutes per side until the internal temperature reaches 165°F, then set aside to rest before slicing into strips.
In a food processor, combine the rinsed chickpeas, tahini, lemon juice, garlic, and the remaining salt and pepper.
Process the mixture until smooth and creamy, adding a tablespoon of water if needed to adjust the consistency.
Slice the pita bread into triangles and toast in a dry pan or oven at 375°F for 5 minutes until golden and crispy.
Transfer the hummus to a small bowl, drizzle with olive oil, and garnish with freshly chopped parsley.
Arrange the sliced chicken, toasted pita points, sliced cucumbers, and halved cherry tomatoes on a platter around the hummus.