Add the chicken, carrots, onion, garlic, and ginger to the slow cooker.
In a bowl, whisk together the coconut milk, chicken broth, green curry paste, fish sauce, sugar, coriander, red pepper flakes, and salt.
Pour the curry sauce into the slow cooker and stir everything together.
Cover and cook on LOW for 4–5 hours or HIGH for 2–3 hours, until the chicken and carrots are tender.
About halfway through cooking, stir in the bell peppers and green beans so they stay a little fresher and don’t become overly soft.
Right before serving, stir in the basil and fresh lime juice.
Serve warm over rice with your favorite toppings.