In a blender, combine the garlic, lemons, and clementines — including the rinds — with the olive oil. Blend on high until the mixture is completely smooth and fragrant. Strain the puree through a fine-mesh sieve into a clean jar or bowl, pressing gently to extract as much infused oil as possible. Discard the solids. The result is a vibrant, aromatic oil with a bright citrusy aroma and subtle garlic depth. Store the oil in the refrigerator for up to two weeks.

Place the cubed chicken in a large mixing bowl. Pour in ½ cup of the prepared citrus-garlic oil and season with kosher salt and freshly ground black pepper. Toss well to ensure every piece of chicken is evenly coated in the zesty marinade. Cover and refrigerate for 30 minutes, allowing the flavors to fully absorb into the meat.

Preheat the grill to medium heat. Thread the marinated chicken pieces onto skewers, spacing them slightly to ensure even cooking. Grill the skewers for 8 to 11 minutes, turning occasionally, until the chicken develops a light char on the edges and is fully cooked through.

Serve the skewers hot, with an optional drizzle of extra citrus-garlic oil for added brightness. These tender, flavorful skewers pair beautifully with rice, couscous, or a fresh garden salad for a light yet satisfying meal.