Place the baby potatoes in an even layer at the bottom of the slow cooker.
Arrange the chicken thighs on top of the potatoes.
In a small bowl, stir together the lemon juice, lemon zest, minced garlic, thyme, rosemary, chicken broth, olive oil, salt, and pepper.
Pour the lemon herb mixture evenly over the chicken and potatoes.
Cover and cook on low for 6 hours.
Add the trimmed green beans to the slow cooker, stir gently to coat them in the liquid, and cook for 1 more hour on low.