Bring first 5 ingredients to a boil in a 3-qt. saucepan over medium heat. Cover, reduce heat to low, and simmer 6 to 8 minutes or until chicken is done.
Remove chicken, garlic, and ginger with a slotted spoon, reserving broth in saucepan. Discard garlic and ginger.
Let chicken cool slightly (10 to 15 minutes); shred chicken.
Return broth to a boil over medium heat.
Add noodles and soy sauce; cook, stirring to separate noodles, 4 to 5 minutes or until just softened.
Remove noodles from broth using tongs, and divide among 6 bowls.
Place chicken and desired toppings on noodles. Return broth to a boil over medium heat; remove from heat, and stir in lime juice. Divide broth among bowls.