Prepare the meat first: cut chicken thighs into large, 1 1/2-inch pieces. Place into a large bowl along with the remaining ingredients. Use a spatula to combine everything together. Cover bowl and refrigerate for a few hours, or overnight.
Skewer chicken meat onto wooden or metal skewers, making sure not to over-crowd the meat. Pre-heat outdoor grill to 475 F or indoor grill pan over medium heat.
Grill chicken for about 20 minutes, turning often to cook evenly. Remove from heat and let the meat rest for 5 minutes before serving.
Simply toss together the cucumber, tomatoes, scallion, dill, salt and olive oil. Serve with chicken.