The portrait is not currently on display.
A series of segments on "The Colbert Report" in 2008 depicted comedian Stephen Colbert's quest to have his portrait accepted by one of the Smithsonian’s museums. The portrait hung in the National Portrait Gallery through April 1, 2008.
On April 1, 2008, the National Museum of American History agreed to display Stephen Colbert's portrait in the "Treasures of American History" exhibition until it closed on April 13, 2008. Later that year, the portrait went on view in the newly renovated National Museum of American History, where it remained on view until September 2009. The portrait returned to public view at the National Museum of American History on December 16, 2010 and was taken down in August 2011 in preparation for the September 11: Remebrance and Reflection event.
Related blog posts:
A real national treasure? (October 2008)
A picture within a picture (November 2008)
Tip/Wag - Art Edition - Brent Glass (December 8, 2010)
Director Brent D. Glass gave Stephen Colbert a surprise phone call on the April 1, 2008, episode of "The Colbert Report."
More video clips:Stephen's search for a home for his portrait (January 2008)
Portrait goes on display in "Treasures of American History" (April 2008)
Director Brent Glass formally accepts the portrait into the Museum's collection (October 2008)