Cut the chicken thighs into 1-inch cubes. Toss in a bowl with olive oil, oregano, lemon zest and juice, chopped parsley, salt, and pepper. Refrigerate for at least 20 minutes.
While the chicken marinates, chop the tomato, cucumber, and bell pepper into rough chunks. Slice the red onion into thin wedges. Combine in a bowl with lemon zest and juice, olive oil, salt, and pepper.
Thread the marinated chicken onto skewers. Grill on a grill pan or outdoor grill over medium-high heat for about 3 minutes per side until charred and cooked through.
Plate the salad, crumble the feta over the top, scatter the olives, and lay the skewers alongside. Serve with Greek yogurt and warm pita.