Does Chicken Broth Break a Meat Fast?

No, it is not considered meat.

The USCCB’s Questions and Answers About Lenten Practices:

Abstinence laws consider that meat comes only from animals such as chickens, cows, sheep or pigs—all of which live on land. Birds are also considered meat. Abstinence does not include meat juices and liquid foods made from meat. Thus, such foods as chicken broth, consomme, soups cooked or flavored with meat, meat gravies or sauces, as well as seasonings or condiments made from animal fat are technically not forbidden. However, moral theologians have traditionally taught that we should abstain from all animal-derived products (except foods such as gelatin, butter, cheese and eggs, which do not have any meat taste).