In a measuring cup, stir together 3 tablespoons olive oil, the garlic, lemon peel, lemon juice, hot sauce and sugar until the sugar dissolves. Pour all but 1/4 cup of the marinade into a large bowl. Season the chicken with salt and pepper, add to the bowl and toss to coat. Cover and let marinate for 30 minutes.
Meanwhile, in a large saucepan of boiling, salted water, cook the green beans until crisp-tender, about 2 minutes; drain.
Heat a grill pan over medium-high heat. Working in batches, grill the chicken, turning once, until cooked through, about 5 minutes. Transfer to a serving platter and drizzle with the reserved 1/4 cup marinade; toss to coat. Cover to keep warm.
Heat the grill pan over medium-high heat. In a small bowl, drizzle the onion with the remaining 1 tablespoon olive oil. Grill the onion, turning occasionally, until tender, about 5 minutes; transfer to the platter. Add the green beans to the grill pan and cook until lightly charred, about 2 minutes; transfer to the serving platter. Lightly toss the chicken with the vegetables and season with salt and pepper.