Bring a quart of water to a boil and add the chicken breast. Cook for ten minutes remove the chicken breast and shred. Add the egg to the boiling water and cook for seven minutes and remove from heat. Let sit out of water for 5 minutes and then peel.
Bring the broth to a boil in a separate pan, add the salt, and garlic clove. Take the broth off the heat.
Slice the onion and jalapeño and add to broth. Add the bean sprouts and cilantro. Put the egg in a break apart and top with lime juice.