Add the carrots, parsnips, sweet potato, and onion to the bottom of the slow cooker.
Place the chicken thighs on top of the vegetables.
Drizzle the olive oil over the chicken and sprinkle with salt and black pepper.
Scatter the minced garlic and chopped rosemary evenly over the chicken and vegetables.
Pour the chicken broth around the edges of the slow cooker.
Cover and cook on low for 6 to 8 hours, until the chicken is tender and the root vegetables are soft.
Serve the chicken and vegetables with a ladle of the cooking broth.