Season chicken with salt and pepper. Place a large Dutch oven or heavy pot with a tight-fitting lid over medium heat.

Add chicken, skin side down, and cook until browned on both sides, about 14 minutes, turning one time in between. Transfer chicken to a plate.

Reduce heat to medium and add onion. Cook until onions are translucent, stirring occasionally, about four minutes. Add the garlic and cook it for about 30 seconds, just until fragrant.

Add chard leaves, leeks, lemon zest, and rice to cook for another minute. Add broth and bring to a boil.

Reduce to a simmer and add salt and pepper. Place chicken, skin side up, on rice mixture and cook, covered, until chicken is cooked through and liquid is almost fully absorbed, about 30–40 minutes.

Turn off heat and allow to sit covered for at least five minutes.