Preheat a grill or grill pan over medium-high heat.
Season the chicken breast with salt, black pepper, and dried oregano.
Grill the chicken breast until cooked through, about 6-8 minutes per side. Once cooked, set aside to cool.
While the chicken is cooking, prepare the salad ingredients: chop the mixed salad greens, halve the cherry tomatoes, dice the cucumber and red bell pepper, finely chop the red onion, pit and chop the Kalamata olives, and crumble the feta cheese.
In a small bowl, whisk together the extra-virgin olive oil, lemon juice, minced garlic, and a pinch of salt and black pepper to make the dressing.
Once the chicken has cooled slightly, chop it into bite-sized pieces.
In a large mixing bowl, combine the chopped chicken, mixed salad greens, cherry tomatoes, cucumber, red bell pepper, red onion, Kalamata olives, and crumbled feta cheese.
Mix well with mayo and lemon juice until everything is evenly coated.
Divide the mixture evenly between the pitas and fold in half.
Serve with carrots and hummus and sweet tea.