Wash and chop the carrots into rounds, trim the green beans, and halve the baby potatoes.
Mince the garlic clove and set aside.
In a small bowl, whisk together the olive oil, sea salt, black pepper, dried rosemary, and dried thyme.
Place the chicken breast in the bottom of the slow cooker and rub with half of the herb and oil mixture.
Add the potatoes, carrots, and green beans around the chicken, then drizzle with the remaining herb mixture and minced garlic.
Pour the chicken broth into the bottom of the slow cooker, being careful not to wash the herbs off the chicken.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours until the chicken is tender and vegetables are soft.
Remove the chicken to rest for 5 minutes before slicing, then serve alongside the vegetables and a spoonful of the cooking juices.