On September 28, the final day of the 2008 regular season and the final game at Shea Stadium, the Mets played the Florida Marlins.
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Chávez's catch at Shea Stadium in Game 7 of the 2006 National League Championship Series is seen by many as one of the most remarkable plays in baseball history.
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On October 3, 2004 Chávez recorded the final out in Montreal Expos history in their 8–1 loss to the New York Mets at Shea Stadium.
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On July 13, 2007, American International Group (the company whose advertisement happened to be on the spot on the left field wall at Shea Stadium where Chávez made the catch) sponsored a special Bobblehead Doll day to commemorate the catch.
Hugo Chávez | Julio César Chávez | Cesar Chavez | Carlos Chávez | Hugo Chavez | Ñuflo de Chávez Province | Endy Chávez | Cindy Chavez | César Chávez | San Javier, Ñuflo de Chávez | Óscar Chávez | Ñuflo de Chávez | Julio Chávez | José Chavéz y Castillo | Cesar Chavez Avenue | Alfredo Chávez | Norma Chávez | Michelle Chavez | Martin Chávez | Maria Chavez-Hernandez | Linda Chavez-Thompson | Jose Chavez y Chavez | Jorge Chávez | Ingrid Chavez | Ignacio Chávez Sánchez | Edward Chavez | Cristian Manuel Chávez | Cristian Gabriel Chávez | Colegio Cesar Chavez | Christian Chávez |
Left fielder Endy Chávez also made an excellent diving play on a flare hit by Ronnie Belliard.
On December 11, 2008 Cleto was traded to the Mariners with Aaron Heilman, Endy Chávez, Jason Vargas, Mike Carp and Ezequiel Carrera in exchange for J. J. Putz, Jeremy Reed and Sean Green.