1337 is the middle building shown in this old (undated) photo that I suspect is from 2005.
The City Paper has an interesting piece on an upcoming (September 9th and 10th) benefit/art installation/music experience at 1337 H Street. Proceeds to go the new artist (live, work, and studio) space at the same location. The City Paper gives the size as 7900 sqft, which is much larger than I would have guessed. The building belongs to restaurant owner (and Thievery Corporation member) Eric Hilton. Hilton has his hands in Marvin, Patty Patty Boom Boom, and American Ice Company. According to the City Paper he plans to open another restaurant or bar in the basement of 1337 H Street.
Bonus points if you can remember when 1337 was an illegal funeral home.