Trial of the Mexican Drug kingpin is the biggest trial in United States history.
Why Brooklyn: El Chapo was indicted in New York in 2009 on charges stemming from a series of drug related contract killing in Queens in 1993. The seat of Federal court district that also includes Queen is in Brooklyn. As stated in New York Times Article.
Explained Reason why El Chapo ended in Brooklyn:
When EL Chapo was indicted in New York in 2009 for drug related murder in 1993 which happened in the Queens.
US District Court (Eastern District OF NY) (EDNY)= Have its jurisdiction on Brooklyn, Queens, Staten Island, Long Island. If there is an issue arising under federal law under the jurisdiction of EDNY that issue will be reported to this district court. As arresting of El Chapo was big issue and he was on a run and EDNY had issued warrant for his arrest that is why he was presented in the federal court in Brooklyn.