Put chicken in a medium pot. Add broth, cover, and bring to a boil over high heat. Bruise lemongrass by chopping it a few times with the back side of a knife (blade up). Bend the stalk in half and add to pot along with ginger and onion. As soon as broth boils, reduce heat to medium and simmer, partially covered, until chicken is cooked through, about 20 minutes more.
Bring a small pot of water to a boil over high heat. Add rice noodles and cook, stirring to keep them from sticking, until just cooked through, about 4 minutes. Drain in a colander and rinse with cold water. Set aside.
Transfer chicken pieces from broth to a large plate to let cool. Add fish sauce and white pepper to broth, cover, and keep warm over lowest heat. Remove and discard lemongrass, ginger, and onion.
When chicken is cool enough to handle, remove skin and bones. Thinly slice meat. Arrange cilantro, lime wedges, bean sprouts, and sliced jalapeño on a platter.
Divide noodles among four large soup bowls. Put some chicken into each bowl, then pour 2 cups hot broth into each bowl. Serve with platter of toppings.