Whisk the olive oil, lemon juice, garlic, salt, and pepper. Pour the marinade over the chicken pieces, then sprinkle the chopped thyme onto the chicken. Toss to coat evenly, then cover and chill at least 2 hours and up to overnight.
Combine the greek yogurt, lemon juice, lemon zest, ground mustard and paprika in a medium sized bowl. Whisk until combined. Taste for seasoning and add salt and pepper if needed. Refrigerate until ready to use. Alternatively, prepare the dip just before serving.
When you are ready to cook, heat a grill over high heat.
If using wooden skewers, place them in a bowl of water to soak for 10 minutes. Thread the chicken onto the skewers, then baste with any remaining marinade.
Grill the skewers over high heat, turning every 3-4 minutes until charred on the outside and cooked through on the inside. Test for doneness with an instant read thermometer - the skewers are ready when they hit an internal temperature of 165*. If the outsides are charring too quickly, move the skewers to a cooler section of the grill to ensure the outsides do not burn before the insides are finished cooking.
Remove the skewers from heat and place on a platter with the yogurt dipping sauce. Squeeze with additional fresh lemon juice and sprinkle with fresh thyme. Serve immediately. The skewers will keep in the fridge in a sealed container for up to 5 days. Reheat by removing the chicken from the skewers and sautéing in a cast iron skillet over medium heat.