If you're traveling through there, federal law applies and you can transport a firearm in a locked box in the trunk though you're likely to be hassled at minimum if stopped. If, however, you're staying there it's a no no.
![NoNo :nono:](./images/smilies/nono.gif)
You must be licensed in DC to own and keep a firearm.
Read all about it here...
http://regnery.com/books/emily-gets-her-gun/
Larry