Add the chicken thighs, onion, garlic, ginger, bruised lemongrass, coconut milk, chicken broth, and fish sauce to the slow cooker.
Stir gently to combine, then cover and cook on low for 5 hours.
Add the green beans to the slow cooker and continue cooking on low for 1 more hour until the beans are tender but still bright.
Remove and discard the lemongrass stalks.
Stir in the lime juice, then ladle the stew into bowls and top with chopped cilantro.