Place 2 lbs. boneless skinless chicken thighs in the bottom of a 6-quart crock pot.
Add ½ of the sliced red onion, 2 large sliced carrots, juice from 1 lemon, 1 teaspoon dried oregano, 1 teaspoon dried basil, 1 teaspoon dried thyme, 1 teaspoon minced garlic, and 1 cup chicken broth.
Cover and cook on Low for 6 hours or High for 3 hours, until the chicken is tender and shreds easily with two forks.
Shred the chicken directly in the crock pot and stir it into the cooking juices and vegetables.
For the Tzatziki:
Peel and deseed 1 cucumber, then grate it with a box grater. If it seems very watery, gently squeeze out the excess moisture with a clean kitchen towel or paper towels.
In a medium bowl, combine 1 cup plain Greek yogurt, the grated cucumber, the remaining ½ of the sliced red onion (finely diced if desired), 1 tablespoon dried dill (or 2 tablespoons chopped fresh dill), ¼ teaspoon salt, and ½ teaspoon minced garlic.
Stir until well combined.
For Serving:
Warm 6 pita breads if desired.
Divide the shredded chicken evenly among the pita breads and top each with the tzatziki sauce. Serve immediately and enjoy.