Start by preparing your vegetables since they require the most prep work. Peel the cucumber, cut it in half lengthwise, and scoop out the seeds with a spoon—this prevents the salad from becoming watery. Finely dice the cucumber into roughly 1/4-inch pieces and place in a fine-mesh strainer set over a bowl. Dice the onion into small pieces, halve the cherry tomatoes, and slice the kalamata olives into 1/4-inch rounds. While the cucumber drains (this removes excess moisture), combine the Greek yogurt, lemon juice, and freshly minced garlic in a large mixing bowl, stirring until smooth and well combined.
Add the shredded or diced rotisserie chicken to the tzatziki base from Step 1, along with the drained cucumber, diced onion, and halved cherry tomatoes. Crumble the feta cheese into bite-sized pieces and add it to the bowl along with the sliced kalamata olives. I like to add the fresh herbs at the very end—sprinkle in the dill and parsley just before chilling so they maintain their vibrant color and flavor. Season with salt and black pepper to taste, then gently fold everything together until evenly combined, being careful not to break up the feta too much.
Cover the salad and refrigerate for at least 30 minutes—this allows the flavors to meld and makes the salad more refreshing to eat. When ready to serve, give the salad a gentle stir to redistribute the tzatziki. Warm the pita bread lightly (in a dry skillet, wrapped in foil in the oven, or directly over a gas flame for 10-15 seconds per side) to make it pliable and easier to fill. Serve the chicken salad alongside or inside the warm pitas, adding an extra dollop of tzatziki on top if desired.