Heat half of the oil in a large deep skillet over medium heat. Saute the chicken in two separate batches until lightly browned. Transfer the chicken to the slow cooker.
Add the rest of the oil to the skillet and saute the onion, carrot, and bell pepper until almost tender, about 4 minutes. Stir in the garlic, ginger, and curry powder and heat through for a few seconds until aromatic. Add in broth, salt, and lemongrass and heat to boiling. Pour into slow cooker, cover, and cook for 3 to 5 hours on high, or 4 to 8 hours on low, until broth is well flavored and the veggies are tender.
Meanwhile mix the coconut milk, peanut butter, soy sauce, brown sugar, and hot sauce to combine. Pour into soup in slow cooker and cook on high for 15 minutes. Stir in cilantro just before serving.