In a 4- to 5-quart pan over high heat, bring broth, onion, celery, garlic, and pepper to a boil. Add pasta and chicken; return to a boil.
Reduce heat to low, cover pan, and simmer until chicken is white in thickest part (cut to test), about 5 minutes. With tongs, lift out breasts and let stand. Continue simmering soup until pasta is tender to bite, about 2 minutes more. Reduce heat to very low and keep soup warm.
When chicken is just cool enough to handle, in about 5 minutes, tear into coarse shreds and return to pan.
Stir lemon juice, parsley, and cilantro into soup. Ladle into wide bowls.
Peel, pit, and thinly slice avocado; add to bowls.