Season the chicken breast evenly with the dried oregano, sea salt, and black pepper.
Heat a non-stick skillet over medium heat and cook the chicken for 6-7 minutes per side until golden and the internal temperature reaches 165°F.
While the chicken cooks, combine the rinsed chickpeas, Greek yogurt, tahini, lemon juice, garlic, and fresh parsley in a food processor.
Process the hummus mixture until it reaches a velvety, smooth consistency, adding a teaspoon of water if needed to adjust the texture.
Slice the cooked chicken into thin strips and cut the cucumber, bell pepper, and carrot into long dipping sticks.
Arrange the warm chicken strips, creamy herb hummus, and fresh vegetables on a large platter and serve immediately.