Lightly coat the inside of slow cooker with olive oil.

Add all ingredients except salt, pepper, chicken, chard, and tomatoes to slow cooker, stirring to combine.

Season chicken with salt and pepper then nestle into slow cooker. Cover and cook until chicken is tender about 3–4 hours on low.

When chicken is done, transfer chicken to plate and tent with aluminum foil to keep warm.

Switch the slow cooker to high then stir Swiss chard and tomatoes into liquid, cover, and cook until chard is wilted, 15 to 20 minutes.

Return chicken and any accumulated juices to slow cooker and season with salt and pepper to taste. Let chicken heat through, about 5 minutes before serving.