While your grill heats to medium-high, prepare all your ingredients: peel and dice the cucumber into 1/2-inch pieces, halve the yellow grape tomatoes, thinly slice the red onion, roughly chop the fresh mint, crumble the feta, and mince both garlic cloves separately (keeping the minced garlic for the chicken marinade separate from the garlic for the dressing). In a small bowl, combine 1.5 tablespoons olive oil, 1 minced garlic clove, oregano, juice from the lemon half, and a pinch of salt and pepper. Add the 1-inch chicken chunks to this marinade and stir to coat evenly. Let the chicken sit for 10 minutes while you finish prepping—this helps the flavors penetrate the meat.

Place the marinated chicken chunks on the preheated medium-high grill. Cook for 4-5 minutes per side until the chicken is cooked through and has nice grill marks. I like to arrange the pieces so they don't crowd the grill—this helps them cook evenly and develop better color. Once cooked, transfer the chicken to a cutting board and let it rest for a few minutes before slicing into strips.

In a separate bowl, whisk together 5 tablespoons olive oil, red wine vinegar, 2 minced garlic cloves, dried dill, salt, and pepper until combined. In a large bowl, combine the diced cucumber, halved tomatoes, sliced red onion, chopped mint, feta crumbles, and kalamata olives. Pour the dressing over the salad and gently toss to combine. For the best flavor, let the salad sit for a minute or two so the dressing can coat everything evenly—this helps the vegetables absorb all those bright Mediterranean flavors.

Cut the pitas in half to create pockets, then toast them lightly on the grill or in a toaster to warm them through and add a subtle char—this prevents them from getting soggy and makes them easier to stuff. Divide the dressed salad from Step 3 among the pita pockets, then top with the grilled chicken strips. Serve immediately while the pitas are still warm.