Prepare the Chicken Marinade: In a medium-sized bowl or a large resealable plastic bag, whisk together the extra virgin olive oil, fresh lemon juice, minced garlic (for marinade), dried oregano, smoked paprika, and ⅓ teaspoon of salt.
Marinate the Chicken: Add the bite-sized chicken pieces to the marinade, ensuring each piece is well-coated. If using a bag, expel excess air and seal it. If using a bowl, cover it tightly. Refrigerate for at least 2 hours, or up to 4 hours, to allow the flavors to permeate the chicken.
Craft the Cool Mint & Cucumber Tzatziki: While the chicken is marinating, prepare the tzatziki. In a separate small bowl, combine the Greek yogurt, grated cucumber (gently squeeze out any excess liquid from the cucumber if it appears very watery), finely chopped fresh mint, white vinegar, minced garlic (for tzatziki), and a pinch of salt. Stir until well blended. Cover and chill in the refrigerator for at least 30 minutes to an hour for the flavors to meld.
Ready the Skewers and Grill: If using wooden skewers, submerge them in cold water for at least 20-30 minutes prior to grilling to prevent them from burning. Preheat your outdoor grill or indoor grill pan to medium-high heat (approximately 375-450°F or 190-230°C). Lightly oil the grill grates if prone to sticking.
Assemble the Skewers: Once the chicken has marinated, thread the pieces onto the prepared skewers, distributing the chicken evenly. Aim for about 4-5 pieces per skewer if using 4 main skewers. Dispose of any remaining marinade.
Grill the Skewers: Place the assembled chicken skewers onto the hot grill. Cook for approximately 6-8 minutes per side, turning occasionally. The chicken should be nicely browned on all sides and cooked through, reaching an internal temperature of 165°F (74°C). Total cooking time will be around 12-16 minutes.
Serve and Savor: Arrange the freshly grilled Athenian Lemon-Herb Chicken Skewers on plates. Serve immediately with a generous dollop of the chilled Cool Mint & Cucumber Tzatziki alongside. These skewers are excellent on their own or can be served with a side of quinoa, a fresh Greek salad, or warm pita bread.