Season chicken with salt and pepper. Heat a large Dutch oven or other heavy pot with a tight-fitting lid over medium-high. Add chicken, skin side down, and cook until browned on both sides, 12 minutes, turning once. With tongs, transfer chicken to a plate.
Reduce heat to medium and add garlic, chard stems, onion, and carrots. Cook, stirring occasionally, until chard stems and onion are translucent, 4 minutes. Add chard leaves, lemon zest, and rice; cook 1 minute. Add broth and bring to a rapid simmer. Reduce to a simmer and season with salt and pepper. Arrange chicken, skin side up, on top of rice mixture and cook, covered, until chicken is cooked through and liquid is absorbed, about 25 minutes. Remove from heat and let sit, 5 minutes. Serve with lemon wedges.