The shirt was worn by the Navy SEAL during the night time raid in which he shot bin Laden to death in 2011 in the garrison town of Abbottabad.
The SEAL who took down bin Laden wore the shirt as he fired the three fatal shots that killed the then al-Qaeda chief.
His identity has never been revealed because of concerns for his safety - and his name will not be included in the display of the shirt, which is brown with a black American flag on the sleeve.
Maloney said that the shirt is an important part of the story of September 11, 2001, from the horror of the terror plot to the eventual payback for bin Laden.
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