Whisk all ingredients in a bowl or pulse in a food processor until smooth. Sauce can be made up to 3-5 days ahead (keep refrigerated until ready to serve).
Assemble and cook chicken skewers
Preheat a grill to medium-high heat (about 375F or 190C) for direct grilling about 15 minutes before cooking. If cooking the skewers indoors, preheat oven to 450 degrees and line a large baking sheet with aluminum foil.
Put the chicken in a medium bowl and toss with the pesto, salt and chili pepper.
Thread the chicken, cheese, zucchini, tomatoes and peppers on skewers, alternating as you go. Aim for 10-12 pieces per skewer.
Put the skewers on the preheated grill and cook until the chicken is cooked through, 3-5 minutes per side. If they're browning too fast, move to the cooler part of the grill and cover to finish cooking. If you're cooking in the oven, bake about 20 minutes, turning once, until the chicken is no longer pink and the cheese is browned.
Spread about 1/4 cup of the yogurt sauce on a large platter. Arrange the skewers on top and squeeze the lemon wedges over. Serve with cucumber, feta and additional sauce on the side.
Substitute with the same amount of red bell pepper, cut into 2-inch pieces.
Halloumi can be tricky to find. Just omit if you prefer, but don't skip feta cheese when serving!