In a large bowl, mix the first 8 ingredients. Add the chicken; toss to coat. Cover and refrigerate for at least 6 hours or overnight. Bring to room temperature before grilling.
In a small skillet, combine the lemon peel, lemon juice and salt. Cover and simmer until the peel is tender, about 10 minutes. Drain. Transfer the peel to a small bowl. Add the EVOO, parsley and lime juice; whisk to make the vinaigrette.
Heat a grill or grill pan over medium-high. Cover grill with foil to prevent sticking. Thread chicken onto 8 metal or soaked wooden skewers; season. Grill until the chicken is browned and cooked through, turning occasionally, 5 to 8 minutes. Drizzle with the vinaigrette before serving.
