Preheat a grill pan over high heat. Season chicken with 1 teaspoon Mediterranean spice and place on grill. Cook, basting with balsamic vinaigrette and turning once, until cooked through, about 2 minutes per side. Season chicken with remaining teaspoon Mediterranean spice and remove from grill; set aside.
Place shredded romaine lettuce and red onions in a medium bowl; drizzle with red-wine vinaigrette and toss to combine.
Top each taco with 1 piece of chicken and garnish with chopped tomatoes, cheese, etc. Season with parsley, basil, and oregano; serve.