This crowd-pleasing dish doesn't contain gluten, dairy, or nuts, so it's suitable for just about everyone to enjoy.
Over a high gas flame, roast peppers until charred, 16 minutes, turning frequently. Transfer to a bowl, cover tightly with plastic wrap, and let steam 20 minutes. Meanwhile, heat a grill or grill pan over medium-high. Clean and lightly oil hot grill. Toss zucchini with 1 1/2 teaspoons oil and season with salt and pepper. Grill zucchini until browned, about 4 minutes, flipping once. Drizzle chicken with 1/2 teaspoon oil, season with salt and pepper, and grill until cooked through, about 6 minutes, flipping once.
Rub peppers with paper towels to remove skin. Stem, seed, and slice into 1/2-inch strips. In a small bowl, whisk together vinegar and 2 tablespoons oil; season with salt and pepper. Stir in currants, artichokes, and parsley. Arrange chicken and vegetables on a serving platter and drizzle with vinaigrette. Serve warm or at room temperature.