Thinly slice about one-fourth of onion to measure ¼ cup. Finely chop the remaining onion.
Melt coconut oil in a medium Dutch oven over medium heat. Add the chopped onion, bell pepper and 1 tablespoon chopped jalapeño; cook, stirring occasionally, until slightly softened, about 2 minutes. Add sweet potato, garlic and ginger; cook, stirring constantly, until fragrant, about 1 minute. Add curry paste, salt and pepper; cook, stirring constantly, until the curry paste is fragrant and turns a few shades darker, about 2 minutes.
Stir in broth and coconut milk; bring to a simmer over medium heat. Cover, and cook until the sweet potato is almost tender, about 10 minutes.
Stir in chicken and green beans. Cook, uncovered, stirring occasionally, until the beans are bright green and tender, about 10 minutes. Remove from heat; stir in cilantro, basil and lime juice.
Divide the soup among 6 bowls. Top with the reserved sliced onion and the remaining 2 tablespoons sliced jalapeño.
