In a large bowl, whisk together olive oil, wine, lemon juice, mint, oregano, and garlic. Add chicken, and toss to coat. Cover, and refrigerate for 1 hour or up to 8 hours.
Heat the griddle to 400°F (200°C). Thread three pieces of chicken each onto a wooden skewer, with pieces just touching each other; season liberally with salt and pepper. Arrange half of the kebabs on the griddle, along with half of the lemons, cut sides down. Cook kebabs, turning as needed, until cooked through and slightly charred on all sides, about 10 minutes. Remove kebabs and lemon halves from the griddle. Cut lemon halves into two wedges each. Repeat with remaining kebabs and lemons. Serve kebabs with grilled lemon wedges.
Variation: Korean Barbecue Chicken Kebabs
Make as directed, omitting all ingredients except chicken and skewers. Marinate chicken in ½ cup (150 grams) Korean red chile paste (also known as gochujang), ½ cup (118 milliliters) soy sauce, 2 tablespoons (26 grams) honey, 2 tablespoons (30 milliliters) toasted sesame oil, and 1 tablespoon (15 milliliters) rice vinegar.
Variation: Tikka Masala Chicken Kebabs
Make as directed, omitting all ingredients except chicken and skewers. Marinate chicken in ½ cup (180 grams) plain yogurt, ¼ cup (168 grams) tomato paste, 1 tablespoon (6 grams) ground coriander, 1 tablespoon (10 grams) ground turmeric, 1 tablespoon (9 grams) kosher salt, 1 tablespoon (6 grams) sweet paprika, and 1 tablespoon (15 milliliters) vegetable oil. Serve kebabs with additional plain yogurt drizzled on top, and sprinkle with finely chopped cilantro.
While the kebabs are great on their own, save any leftovers to stuff inside pita bread along with pickles, lettuce, tomato, and yogurt for a pita sandwich.