Season the chicken breast evenly with sea salt, black pepper, and dried oregano.
Heat a grill pan or cast-iron skillet over medium-high heat and cook the chicken for 5-6 minutes per side until the internal temperature reaches 165°F.
While the chicken rests, prepare the hummus by combining the chickpeas, tahini, lemon juice, and garlic in a high-speed blender or food processor.
Blend the hummus until completely smooth, adding 1-2 tablespoons of water if needed to reach a velvety consistency.
Finely chop the fresh parsley and dill, then fold them into the hummus for a burst of fresh flavor.
Dice the cucumber and halve the cherry tomatoes, tossing them together in a small bowl.
Spread the herb hummus in a wide circle on a plate, top with the sliced grilled chicken, and pile the cucumber-tomato salad on the side.
Finish the dish with a drizzle of high-quality extra virgin olive oil.