Make the marinade: In a large bowl, whisk together the Greek yogurt, olive oil, fresh lemon juice, lemon zest, minced garlic, dried oregano, dried thyme, ground cumin, smoked paprika, kosher salt, black pepper, and chopped dill. Stir until well combined.
Cut the chicken into strips: Cut the boneless, skinless chicken thighs (or breasts) into long, even strips rather than cubes. This makes it easier to fold the chicken onto the skewer for thicker, more even pieces. *If needed, use a meat mallet to pound out thicker parts of the thighs to make them more even.
Marinate the chicken: Add the chicken strips to the marinade and toss to coat every piece fully. Cover and refrigerate for at least 2 hours, but no more than 24 hours.
Skewer the chicken: Thread each strip of chicken onto a skewer in an over-and-under, folding motion so the strip bunches into one thick, compact piece rather than lying flat. Continue threading the chicken strips on each skewer until full. We were able to get about 4 skewers from 2 pounds of chicken.
Preheat the grill: Heat your grill or coals to medium to medium-high heat. Set up an indirect and a direct heat zone.
Grill the skewers: Place the skewers over direct heat and grill, rotating occasionally, until the chicken is charred in spots and cooked through to an internal temperature of 180-185°F for boneless thighs or 165℉ for breasts. *If the chicken starts to burn, transfer to the indirect heat side of the grill for slower cooking.
Rest and serve: Remove the skewers from the grill and let the chicken rest for about 5-10 minutes before serving. Serve with warm pita, tzaziki sauce, Mediterranean-style veggies, or your favorite toppings.