In a large bowl, combine olive oil, lemon juice, garlic, oregano, thyme, paprika, salt, and pepper.
Add chicken pieces to the marinade and toss until evenly coated. Cover and refrigerate for at least 30 minutes.
While the chicken marinates, prepare the tzatziki by mixing Greek yogurt, grated cucumber, olive oil, lemon juice, garlic, dill, and salt in a bowl. Refrigerate until ready to serve.
Preheat a grill or grill pan to medium-high heat.
Thread the marinated chicken pieces onto skewers.
Grill the skewers for 12 to 15 minutes, turning occasionally, until the chicken is fully cooked and lightly charred.
Remove from the grill and allow the skewers to rest for a few minutes before serving.